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For every two statements P and Q, use truth tables to verify the following. (a) P Q ( P)

Chapter 1, Problem 12

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QUESTION:

For every two statements P and Q, use truth tables to verify the following. (a) P Q ( P) ( Q). (b) P Q (P Q) (( P) ( Q)). (c) (P Q) P ( Q).

Questions & Answers

QUESTION:

For every two statements P and Q, use truth tables to verify the following. (a) P Q ( P) ( Q). (b) P Q (P Q) (( P) ( Q)). (c) (P Q) P ( Q).

ANSWER:

Step 1 of 3

(a)

Consider the given Boolean expression,

The biconditional expression of P and Q is . It means P is necessary and sufficient for Q.          

The truth table for verifying the given expression:

Consider the L.H.S part .

 

 

 

 

T

T

T

T

T

T

F

F

T

F

F

T

T

F

F

F

F

T

T

T

Consider the R.H.S part

 

 

 

 

 

 

T

F

T

F

T

T

T

T

F

F

T

T

F

F

F

T

T

F

F

T

F

F

T

F

T

T

T

T

Hence, the L.H.S and R.H.S are the same. So, .

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