# Prove that the following statement pattern is equivalent : (p ∨ q)  r and (p → r) ∧ (q → r) - Mathematics and Statistics

Sum

Prove that the following statement pattern is equivalent :

(p ∨ q) →  r and (p → r) ∧ (q → r)

#### Solution

Truth table given is as follows:

 1 2 3 4 5 6 7 8 p q r A=p vv q B=p->r C=q->r A->r B ^^ C T T T T T T T T T T F T F F F F T F T T T T T T T F F T F T F F F T T T T T T T F T F T T F F F F F T F T T T T F F F F T T T T

In the above truth table all the entries in the columns of

(p ∨ q) →  r and (p → r) ∧ (q → r) are identical.

(p ∨ q) →  r ≡ (p → r) ∧ (q → r)

Concept: Statement Patterns and Logical Equivalence
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