Engineering
Mathematics
Logical Operator Reasoning AND and OR
Algebra of Statements
Logical Operator Reasoning Conditional and Bi Conditional
Question
If the boolean expression (p ⊕ q) ∧ (~ p Θ q) is equivalent to p ∧ q, where ⊕ ∈ [∧,∨], then the ordered pair (⊕, Θ) is:
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Solution
Check all option repeatedly
(i) (A ∧ B) ∧ (~ A ∨ B) ≡ A ∧ (B ∧ (~ A ∨ B))
≡ A ∧ (B) ≡ A ∧ B
⇒ (i) is correct
(ii) (A ∧ B) ∧ (~ A ∨ B) ≡ (A ∧ ~ A) ∧ B
≡ f ∧ B ≡ f
(iii) (A ∨ B) ∧ (~ A ∨ B) ≡ B
(iv) (A ∨ B)(~ A ∨ B)
≡ B ∨ (A ∧ ~ A) = B ∨ f ≡ f
⇒ only (1) is correct