p ∧ p ≡ pp ∨ p ≡ p
To prove that p ∧ p ≡ pp ∨ p ≡ p, we can use the laws of Boolean algebra to simplify the expressions on both sides of the equation
To prove that p ∧ p ≡ pp ∨ p ≡ p, we can use the laws of Boolean algebra to simplify the expressions on both sides of the equation.
1. Simplifying p ∧ p:
p ∧ p is the conjunction (logical AND) of p with itself. In Boolean algebra, when both operands of AND are true, the result is true; otherwise, it is false. Since p is assumed to be true, p ∧ p is also true.
2. Simplifying pp ∨ p:
pp ∨ p is the disjunction (logical OR) of pp with p. In Boolean algebra, when at least one of the operands of OR is true, the result is true. Since p is assumed to be true, pp will also be true. Therefore, pp ∨ p is true.
3. Simplifying p:
Since p is assumed to be true, p is true.
By comparing the simplified expressions on both sides of the equation, we can see that they are all true (p), which proves that p ∧ p ≡ pp ∨ p ≡ p.
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