p ∧ T ≡ pp ∨ F ≡ p
To prove that p ∧ T ≡ pp ∨ F ≡ p, we can use truth tables:
First, let’s analyze p ∧ T:
p | T | p ∧ T
–|—|——
T | T | T
F | T | F
We can clearly see that p ∧ T will always result in just p itself
To prove that p ∧ T ≡ pp ∨ F ≡ p, we can use truth tables:
First, let’s analyze p ∧ T:
p | T | p ∧ T
–|—|——
T | T | T
F | T | F
We can clearly see that p ∧ T will always result in just p itself.
Now, let’s analyze pp ∨ F:
p | p | pp ∨ F
–|—|——-
T | T | T
F | F | F
We can clearly see that pp ∨ F will also always result in just p itself.
Therefore, we have proven that p ∧ T ≡ pp ∨ F ≡ p, since in both cases we get the same result: p.
More Answers:
Exploring the Laws of Boolean Algebra: Proving Equations using Associative LawProving Equivalence using Truth Tables: p ∧ (q ∨ r ) ≡ (p ∧ q) ∨ (p ∧ r ), and p ∨ (q ∧ r ) ≡ (p ∨ q) ∧ (p ∨ r )
Equivalence Proof: Simplifying p ∧ (p ∨ q) ≡ p
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