Question

Verify each of the following using a truth table:

An implication's converse is equivalent to its inverse.

An implication is equivalent to its contrapositive.

An implication is not equivalent to its converse.

Answer 1

A) an impliation's converse is equivalent to its inverse.

implication--- A -->B.

CONVERSE-- B-->A

INVERSE : ~A-->~B

A	B	~A	~B	A-->B	B-->A	~A-->~B
T	T	F	F	T	T	T
T	F	F	T	F	T	T
F	T	T	F	T	F	F
F	F	T	T	T	T	T

B-->A = ~A-->~B

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An implication is equivalent to its contrapositive.

IMPLICATION--- A -->B.

CONTRAPOSITIVE= ~B-->~A

A	B	~A	~B	A-->B	~B-->~A
T	T	F	F	T	T
T	F	F	T	F	F
F	T	T	F	T	T
F	F	T	T	T	T

A-->B = ~B -->~A

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An implication is not equivalent to its converse.

IMPLICATION : A-->B

CONVERSE : B-->A

A	B	A-->B	B-->A
T	T	T	T
T	F	F	T
F	T	T	F
F	F	T	T

A-->B IS NOT EQUIVALENT B-->A