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

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Sum

Prove that the following statement pattern is equivalent :

(p ∨ q) →  r and (p → r) ∧ (q → r)

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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
  Is there an error in this question or solution?

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