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.