The boolean expression ((p∧q)∨(p∨∼q))∧(∼p∧∼q) is equivalent to:
A
p∧(∼q)
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B
p∨(∼q)
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C
(∼p)∧(∼q)
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D
p∧q
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Solution
The correct option is C(∼p)∧(∼q) Solving it using venn diagram analogy i.e., '∧' denotes intersection and ′∨′ denotes union. So, considering the venn diagram for two sets p and q as represnted below ∴p∧q={b};∼q={a,d},∼p={c,d} p∨∼q={a,b}∨{a,d}={a,b,d} ∼p∧q={c,d}∧{b,c}={c} ∴((p∧q)∨(p∨q))={b}∨{a,b,d}={a,b,d}
The Boolean expression ((p∧q)∧(p∨∼q))∧(∼p∼q) is - ={a,b,d}∧{d} ={d} =∼p∧∼q(∵∼p∧∼q={d})