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For each of the pairs of statements i)-iv) below, do the appropriate one of the following: a) give an explanation why the two statements are logically equivalent; or b) give an explanation why one statement implies the other, and give a pair of predicates for p(x) and q(x) which shows that the two statements are not logically equivalent; or c) give two pairs of predicates for p(x) and q(x) which together show that neither state- nd 90) which to ment implies the other. -(p(x) and g(x))" and "-p(x) and -q(x)". ii) “(3x) (p(x) and g(x))" and "(3x) (p(x)) and (3 x) (g(x))". iii) (3x) (p(x) or q(x))" and "(V x) (~p(x)) ⇒ (3 x) (g(x))". iv) "(x) (3 y) (p(x, y))" and "(3 y) (Vx) (p(x, y))".

For each of the pairs of statements i)-iv) below, do the appropriate one of the following: a) give an explanation why the two statements are logically equivalent; or b) give an explanation why one statement implies the other, and give a pair of predicates for p(x) and q(x) which shows that the two statements are not logically equivalent; or c) give two pairs of predicates for p(x) and q(x) which together show that neither state- nd 90) which to ment implies the other. -(p(x) and g(x))" and "-p(x) and -q(x)". ii) “(3x) (p(x) and g(x))" and "(3x) (p(x)) and (3 x) (g(x))". iii) (3x) (p(x) or q(x))" and "(V x) (~p(x)) ⇒ (3 x) (g(x))". iv) "(x) (3 y) (p(x, y))" and "(3 y) (Vx) (p(x, y))".

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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i).- iii)

For each of the pairs of statements i)-iv) below, do the appropriate one of the following: a) give an explanation why the two statements are logically equivalent; or b) give an explanation why one statement implies the other, and give a pair of predicates for p(x) and q(x) which shows that the two statements are not logically equivalent; or c) give two pairs of predicates for p(x) and q(x) which together show that neither state- ment implies the other. i) "-(p(x) and q(x))" and "-p(x) and -q(x)". ii) "(3x) (p(x) and g(x))" and "(3x) (p(x)) and (3 x) (g(x))". iii) "(x) (p(x) or q(x))" and "(V x) (~p(x)) ⇒ (3 x) (q(x))”. iv) "(Vx) (3 y) (p(x, y))" and "(3 y) (V x) (p(x, y))".
Transcribed Image Text:For each of the pairs of statements i)-iv) below, do the appropriate one of the following: a) give an explanation why the two statements are logically equivalent; or b) give an explanation why one statement implies the other, and give a pair of predicates for p(x) and q(x) which shows that the two statements are not logically equivalent; or c) give two pairs of predicates for p(x) and q(x) which together show that neither state- ment implies the other. i) "-(p(x) and q(x))" and "-p(x) and -q(x)". ii) "(3x) (p(x) and g(x))" and "(3x) (p(x)) and (3 x) (g(x))". iii) "(x) (p(x) or q(x))" and "(V x) (~p(x)) ⇒ (3 x) (q(x))”. iv) "(Vx) (3 y) (p(x, y))" and "(3 y) (V x) (p(x, y))".
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