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![maths - Reasoning Complete Rules Mathemarical 1. STATEMENT २. SIMPLE & COMPOUND STATEMENTS Simple sfafemenf A sfqfement is & senfence thqt is cannof be broken false buf nof both true further eifher Or using formed Compound sfafemenf Examples: logical connecfives 2 + 3 = 5 (True) is an even number (False) 4. TRUTH VALUES TABLE (SUMMARY) pAq pVq ٥»٩ p<q ३. LOGICAL CONNECTIVES =٥ p FTF (a) Negation (-p) = T If p is True; -p is false F If p is false -p is frue. ٤ T F F T ٤ (b) Conjunction (p^q) Read as p AND q 5. TAUTOLOGY & CONTRADICTION True only when both p and are Tautology always frue True dlways false Contradiction (c) Disjunction (p ٧و) Read as p OR False only when both p and 6. CONVERSE INVERSE & CONTRAPOSITIVE are false For p -> ৭: Converse - q p (d) Implication (p > q) Inverse 7p 7q [f P, then q Read as Confraposifive > -q 7p 2 False only when p is True ond ৭ contrapositive] p =0 is fdlse; (e) Biconditional (p < 9) 8. QUANTIFIERS p if qnd only if q" Read as (a) Universal Quanfifier 7 VALID & INVALID ARGUMENTS for all Meaning: An argument is valid if the conclusion (b) Existential Quantifier (3) logicqlly follows from premises.. Meaningः there exists 9. NEGATION OF STATEMENTS WITH 0. IMPORTANT POINTS QUANTIFIERS definife A statement must havel truth value -(Vx p(x)) = Jx -p(x) Mathematical reasoning is logic-based} -(3x p(x)) = Vx -p(x) not cdlculdtion-bused verify compound help Trufh tqbles statements Reasoning Complete Rules Mathemarical 1. STATEMENT २. SIMPLE & COMPOUND STATEMENTS Simple sfafemenf A sfqfement is & senfence thqt is cannof be broken false buf nof both true further eifher Or using formed Compound sfafemenf Examples: logical connecfives 2 + 3 = 5 (True) is an even number (False) 4. TRUTH VALUES TABLE (SUMMARY) pAq pVq ٥»٩ p<q ३. LOGICAL CONNECTIVES =٥ p FTF (a) Negation (-p) = T If p is True; -p is false F If p is false -p is frue. ٤ T F F T ٤ (b) Conjunction (p^q) Read as p AND q 5. TAUTOLOGY & CONTRADICTION True only when both p and are Tautology always frue True dlways false Contradiction (c) Disjunction (p ٧و) Read as p OR False only when both p and 6. CONVERSE INVERSE & CONTRAPOSITIVE are false For p -> ৭: Converse - q p (d) Implication (p > q) Inverse 7p 7q [f P, then q Read as Confraposifive > -q 7p 2 False only when p is True ond ৭ contrapositive] p =0 is fdlse; (e) Biconditional (p < 9) 8. QUANTIFIERS p if qnd only if q" Read as (a) Universal Quanfifier 7 VALID & INVALID ARGUMENTS for all Meaning: An argument is valid if the conclusion (b) Existential Quantifier (3) logicqlly follows from premises.. Meaningः there exists 9. NEGATION OF STATEMENTS WITH 0. IMPORTANT POINTS QUANTIFIERS definife A statement must havel truth value -(Vx p(x)) = Jx -p(x) Mathematical reasoning is logic-based} -(3x p(x)) = Vx -p(x) not cdlculdtion-bused verify compound help Trufh tqbles statements - ShareChat](https://cdn4.sharechat.com/bd5223f_s1w/compressed_gm_40_img_221358_df92325_1771378219705_sc.jpg?tenant=sc&referrer=user-profile-service%2FrequestType50&f=705_sc.jpg "maths - Reasoning Complete Rules Mathemarical 1. STATEMENT २. SIMPLE & COMPOUND STATEMENTS Simple sfafemenf A sfqfement is & senfence thqt is cannof be broken false buf nof both true further eifher Or using formed Compound sfafemenf Examples: logical connecfives 2 + 3 = 5 (True) is an even number (False) 4. TRUTH VALUES TABLE (SUMMARY) pAq pVq ٥»٩ p<q ३. LOGICAL CONNECTIVES =٥ p FTF (a) Negation (-p) = T If p is True; -p is false F If p is false -p is frue. ٤ T F F T ٤ (b) Conjunction (p^q) Read as p AND q 5. TAUTOLOGY & CONTRADICTION True only when both p and are Tautology always frue True dlways false Contradiction (c) Disjunction (p ٧و) Read as p OR False only when both p and 6. CONVERSE INVERSE & CONTRAPOSITIVE are false For p -> ৭: Converse - q p (d) Implication (p > q) Inverse 7p 7q [f P, then q Read as Confraposifive > -q 7p 2 False only when p is True ond ৭ contrapositive] p =0 is fdlse; (e) Biconditional (p < 9) 8. QUANTIFIERS p if qnd only if q\" Read as (a) Universal Quanfifier 7 VALID & INVALID ARGUMENTS for all Meaning: An argument is valid if the conclusion (b) Existential Quantifier (3) logicqlly follows from premises.. Meaningः there exists 9. NEGATION OF STATEMENTS WITH 0. IMPORTANT POINTS QUANTIFIERS definife A statement must havel truth value -(Vx p(x)) = Jx -p(x) Mathematical reasoning is logic-based} -(3x p(x)) = Vx -p(x) not cdlculdtion-bused verify compound help Trufh tqbles statements Reasoning Complete Rules Mathemarical 1. STATEMENT २. SIMPLE & COMPOUND STATEMENTS Simple sfafemenf A sfqfement is & senfence thqt is cannof be broken false buf nof both true further eifher Or using formed Compound sfafemenf Examples: logical connecfives 2 + 3 = 5 (True) is an even number (False) 4. TRUTH VALUES TABLE (SUMMARY) pAq pVq ٥»٩ p<q ३. LOGICAL CONNECTIVES =٥ p FTF (a) Negation (-p) = T If p is True; -p is false F If p is false -p is frue. ٤ T F F T ٤ (b) Conjunction (p^q) Read as p AND q 5. TAUTOLOGY & CONTRADICTION True only when both p and are Tautology always frue True dlways false Contradiction (c) Disjunction (p ٧و) Read as p OR False only when both p and 6. CONVERSE INVERSE & CONTRAPOSITIVE are false For p -> ৭: Converse - q p (d) Implication (p > q) Inverse 7p 7q [f P, then q Read as Confraposifive > -q 7p 2 False only when p is True ond ৭ contrapositive] p =0 is fdlse; (e) Biconditional (p < 9) 8. QUANTIFIERS p if qnd only if q\" Read as (a) Universal Quanfifier 7 VALID & INVALID ARGUMENTS for all Meaning: An argument is valid if the conclusion (b) Existential Quantifier (3) logicqlly follows from premises.. Meaningः there exists 9. NEGATION OF STATEMENTS WITH 0. IMPORTANT POINTS QUANTIFIERS definife A statement must havel truth value -(Vx p(x)) = Jx -p(x) Mathematical reasoning is logic-based} -(3x p(x)) = Vx -p(x) not cdlculdtion-bused verify compound help Trufh tqbles statements - ShareChat")
![english - SIMPLE PAST TENSES 66 99 DEFINITION -+ Ximble_Past_Tense_is_used_to_expness an past . in_thel ہcion Combteted STRUCTURE .0- V2/V+ ed Subject AHlinmative_Sentence + played lootball . Examble She did not + Vt Negalive Sentence Subject + bootball . bly Examble She did not Subject + Vt ? Inteuegotive Sentence Did Dootball ? blay Cxamble Did Ahe USES Combleted action past Delinite_past_time] PRESENT PAST TIME WORDS444,4444,4444451 night , 006 , An 2020 Jestexuday last U8e V2 % -ed vetm in oltimative _sentences 7@ SIMPLE PAST TENSES 66 99 DEFINITION -+ Ximble_Past_Tense_is_used_to_expness an past . in_thel ہcion Combteted STRUCTURE .0- V2/V+ ed Subject AHlinmative_Sentence + played lootball . Examble She did not + Vt Negalive Sentence Subject + bootball . bly Examble She did not Subject + Vt ? Inteuegotive Sentence Did Dootball ? blay Cxamble Did Ahe USES Combleted action past Delinite_past_time] PRESENT PAST TIME WORDS444,4444,4444451 night , 006 , An 2020 Jestexuday last U8e V2 % -ed vetm in oltimative _sentences 7@ - ShareChat](https://cdn4.sharechat.com/bd5223f_s1w/compressed_gm_40_img_246156_2ad05135_1771335244765_sc.jpg?tenant=sc&referrer=user-profile-service%2FrequestType50&f=765_sc.jpg "english - SIMPLE PAST TENSES 66 99 DEFINITION -+ Ximble_Past_Tense_is_used_to_expness an past . in_thel ہcion Combteted STRUCTURE .0- V2/V+ ed Subject AHlinmative_Sentence + played lootball . Examble She did not + Vt Negalive Sentence Subject + bootball . bly Examble She did not Subject + Vt ? Inteuegotive Sentence Did Dootball ? blay Cxamble Did Ahe USES Combleted action past Delinite_past_time] PRESENT PAST TIME WORDS444,4444,4444451 night , 006 , An 2020 Jestexuday last U8e V2 % -ed vetm in oltimative _sentences 7@ SIMPLE PAST TENSES 66 99 DEFINITION -+ Ximble_Past_Tense_is_used_to_expness an past . in_thel ہcion Combteted STRUCTURE .0- V2/V+ ed Subject AHlinmative_Sentence + played lootball . Examble She did not + Vt Negalive Sentence Subject + bootball . bly Examble She did not Subject + Vt ? Inteuegotive Sentence Did Dootball ? blay Cxamble Did Ahe USES Combleted action past Delinite_past_time] PRESENT PAST TIME WORDS444,4444,4444451 night , 006 , An 2020 Jestexuday last U8e V2 % -ed vetm in oltimative _sentences 7@ - ShareChat")
![grammer - FUTURE CoNTINUOUS TENSES 99 DEEINITION % 49 ೦2 ~ 4 + {೦ an action that Futuie Continuous Tense shows will be going onat a specilic time in the Jutut 0600 STRUCTURE AHumative Sentence Vingying Subject willbe + + night: at Example She ul be Negative Sentence Vsingying Subject will not_be + + night Example She ull not be 0 Tntertaative Sentence Ving ? Subject be + + 7 gtudying at night ? Example Will_she_bel USES Action_in_pnogness_in_lutute] butwte Action in pugtt in PRESENT FUTURE TIME WORDS-824848484842424242 24244 at this Zime tomoviow, at 5pm Zomoiow wilL be' belcu vexb + ing Use FUTURE CoNTINUOUS TENSES 99 DEEINITION % 49 ೦2 ~ 4 + {೦ an action that Futuie Continuous Tense shows will be going onat a specilic time in the Jutut 0600 STRUCTURE AHumative Sentence Vingying Subject willbe + + night: at Example She ul be Negative Sentence Vsingying Subject will not_be + + night Example She ull not be 0 Tntertaative Sentence Ving ? Subject be + + 7 gtudying at night ? Example Will_she_bel USES Action_in_pnogness_in_lutute] butwte Action in pugtt in PRESENT FUTURE TIME WORDS-824848484842424242 24244 at this Zime tomoviow, at 5pm Zomoiow wilL be' belcu vexb + ing Use - ShareChat](https://cdn4.sharechat.com/bd5223f_s1w/compressed_gm_40_img_248168_298bc28_1771205246915_sc.jpg?tenant=sc&referrer=user-profile-service%2FrequestType50&f=915_sc.jpg "grammer - FUTURE CoNTINUOUS TENSES 99 DEEINITION % 49 ೦2 ~ 4 + {೦ an action that Futuie Continuous Tense shows will be going onat a specilic time in the Jutut 0600 STRUCTURE AHumative Sentence Vingying Subject willbe + + night: at Example She ul be Negative Sentence Vsingying Subject will not_be + + night Example She ull not be 0 Tntertaative Sentence Ving ? Subject be + + 7 gtudying at night ? Example Will_she_bel USES Action_in_pnogness_in_lutute] butwte Action in pugtt in PRESENT FUTURE TIME WORDS-824848484842424242 24244 at this Zime tomoviow, at 5pm Zomoiow wilL be' belcu vexb + ing Use FUTURE CoNTINUOUS TENSES 99 DEEINITION % 49 ೦2 ~ 4 + {೦ an action that Futuie Continuous Tense shows will be going onat a specilic time in the Jutut 0600 STRUCTURE AHumative Sentence Vingying Subject willbe + + night: at Example She ul be Negative Sentence Vsingying Subject will not_be + + night Example She ull not be 0 Tntertaative Sentence Ving ? Subject be + + 7 gtudying at night ? Example Will_she_bel USES Action_in_pnogness_in_lutute] butwte Action in pugtt in PRESENT FUTURE TIME WORDS-824848484842424242 24244 at this Zime tomoviow, at 5pm Zomoiow wilL be' belcu vexb + ing Use - ShareChat")