show that S \/ R is in placed by P \/ Q, P -> R and ( Q -> S)

Question

boolean algreba

Answer 1

For any Booleans a and b, the following truth table applies:

a	b	a→b
F	F	F
F	T	T
T	F	F
T	T	T

Therefore P→R (if P, then R) is equivalent to R; and Q→S is equivalent to S.

S∨R is equivalent to R∨S (commutativity of the Boolean-OR operation).

P∨Q≡R∨S≡(P→R)∨(Q→S).