Solution Found!
For every two statements P and Q, use truth tables to verify the following. (a) P Q ( P)
Chapter 1, Problem 12(choose chapter or problem)
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 .
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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
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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, .