Question

Which logical equivalence is an example of the Distributive law?

a. (p^-q)v(pv-r)=((p^^q)vp)v-r
b. (pv-q)^(pv-r)=(pv-r)^(pv-q)
c. (pv-q)^(pv-r)=pv(q^-)
d. (pv-q)^(pv-r)=(--pv-q)^(pv-r)

Answer 1

The Distributive law states that (p AND q) OR (p AND r) = p AND (q OR r). Option b. ((p OR q) AND (p OR r)) = ((p OR r) AND (p OR q)) is an example of the Distributive law.

Step-by-step explanation:

The Distributive law states that for any three propositions p, q, and r, the following equivalence holds:

(p AND q) OR (p AND r) = p AND (q OR r)

This means that distributing the AND operator over the OR operator in the left-hand side of the equation is equivalent to distributing the AND operator over each operand in the right-hand side.

Option b. (p OR q) AND (p OR r) = (p OR r) AND (p OR q) is an example of the Distributive law. In this case, the expression on the left-hand side distributes the AND operator over the OR operator, resulting in the expression on the right-hand side.