Kenneth Rosen Edition 7 Exercise 1.3 Question 13 (Page No. 35)

Question

Use truth tables to verify the absorption laws.

a) p ∨ (p ∧ q) ≡ p

b) p ∧ (p ∨ q) ≡ p

Comments

you can simply draw truth table and verify it,why it is asked in doubt??

Answer 1

By truth table, simply take all possible combinations of p and q and find the corresponding truth values of the given questions. 

However a better method to solve such questions is the BY CASE method.

For (a), Take 2 cases i.e P = True and P = False.

When P = True,

                          LHS = T v (T ^ q) = T v anything = T

                          RHS = p = T

                          Hence its satisfying for this case, let’s check for the other case.

When P = False,

                         LHS = F V (F ^ q) = F v F = F

                         RHS = F

                         Hence its satisfying for this case too.

 

Similarly, you can check for option (b).                         

Comments

“However a better method to solve such questions is the BY CASE method.

Why is it better?

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To construct a truth table you have to deal with all the cases of P and Q. You have to then formulate the truth values for p ^ q followed by p v (p ^ q) which is very cumbersome.

Thus, using the by case method, we can always use some of the stuff that we know, like anything V true = True. 

This method helps to solve questions faster.

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In short you avoided ‘Q’ column in the truth table construction right?

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Yeah in this case, it is happening that way.