Q75.The Boolean expression ((p ∧q) ∨(p ∨~q)) ∧(~p ∧~q) is equivalent to (1) p ∧(~q) (2) (~p) ∧(~q) (3) p ∨(~q) (4) p ∧q
What This Question Tests
Simplify the given Boolean expression using logical equivalences and properties of logical connectives like distributive law and De Morgan's laws. A truth table can also be used, but algebraic simplification is usually faster for complex expressions.
Concepts Tested
Formulas Used
p∧(q∨r) = (p∧q)∨(p∧r)
(p∨q)∧(~p∧~q) is a contradiction
De Morgan's laws: ~(p∧q) = ~p∨~q
Identity laws
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📋 Question Details
- Chapter
- Mathematical Reasoning
- Topic
- Boolean algebra and logical equivalence
- Year
- 2019
- Shift
- 12 Jan Shift 1
- Q Number
- Q75
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 14: Mathematical Reasoning
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