Question

Prove the following equivalencies by writing an equivalence proof (i.e., start on one side and use known equivalencies to get to the other side). Label each step of your proof to explain the equivalency.

1. A ∨ B → C ≡ (A → C) ∧ (B → C)
2. A → B ∨ C ≡ (A → B) ∨ (A → C)

Answer 1

SOLUTION -

(A)

We need to show thatby using other equivalences.

The given statement is

We take left part of the above statement

Using, we get

On applying law of negation, we get

On applying distributive property, we get

This can be written as

.

Hence, we proved

(B)

We need to show thatby using other equivalences.

The given statement is .

We take left part of the above statement

Using, we get

This can be written as

Using, we get

Hence, we proved

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