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3 years ago

: Show that the propositions (p ∨ q) ∧ (¬p ∨ r) and (p ∧ r) ⊕ (¬p ∧ q) are logically equivalent.

Computers and Technology

1 answer:

Ipatiy [6.2K]3 years ago

3 0

Answer:

$(p\vee q)\wedge(\neg p\vee r)\equiv(p\wedge r)\vee(\neg p\wedge q)$

Explanation:

The statements are logically equivalent if they have the same truth tables. So let´s use truth tables in order to determine if they are logically equivalent or not:

The picture that I attached you shows the truth table for each case. As you can see in the highlight columns:

$(p\vee q)\wedge(\neg p\vee r)\equiv(p\wedge r)\vee(\neg p\wedge q)$

They are logically equivalent because they have exactly the same truth values between each other. Hence, we can conclude that they are logically equivalent.

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