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Prove the two logic distributive laws. (a)x∧(y∨z)≡(x∧y)∨(x∧z).

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Final answer:

To prove the two logic distributive laws (a) x∧(y∨z)≡(x∧y)∨(x∧z), we can use the distributive property of multiplication over addition.

Step-by-step explanation:

The two logic distributive laws are:

(a) x∧(y∨z) ≡ (x∧y)∨(x∧z)

To prove this law, we can use the distributive property of multiplication over addition. Step 1: Distribute x over the parentheses: (x∧y)∨(x∧z). Step 2: Simplify using the distributive property: (x∧y)∨(x∧z) = x∧y∨x∧z. Step 3: Use the commutative property of conjunction to rearrange the terms: x∧x∧y∨z. Step 4: Combine the x terms: x∧x = x. Step 5: Simplify the expression: x∧y∨z.

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