Question

The "absorption law" (theorem 2.1.1 in our book) states that p V (p Aq) is logically equivalent to p. Construct a truth table to show these statements are equivalent.

Answer 1

According to the Law of Absorption, these 2 expressions are equivalent:

p ∨ (p ∧ q) = p

Truth Table:

(see the image attached)

Explanation:

To construct the Truth Table you can consider the 4 possible combinations of states that p and q could have, that is

1. p=T, q=T

2. p=T, q=F

3. p=F, q=T

4. p=F, q=F

Then you can calculate p ∨ (p ∧ q) = p for each combination

1. T ∨ (T ∧ T) = T

2. T ∨ (T ∧ F) = T

3. F ∨ (F ∧ T) = F

4. F ∨ (F ∧ F) = F

You can see that the previous values are the same states that p has, you can also see it in the table attached.