Explanation
Step -1: After applying associative and distributive law
Given, (p∧q)∨(∼p∧q)∨(∼q∧r)
≡[(p∨∼p)∧q]∨(∼q∧r) [∵(a∨b)∧c≡(a∧c)∨(b∧c)]
Step -2: Apply complement law
≡(T∧q)∨(∼q∧r) [∵(a∨∼a)≡T]
Step -3:Apply identity law
≡q∨(∼q∧r) [∵(T∧a)≡q]
Step -4: Apply distributive law
≡(q∨∼q)∧(q∨r) [∵(a∧b)∨c≡(a∨c)∧(b∨c)]
Step -5: Apply complement law
≡T∧(q∨r) [∵(a∨∼a)≡T]
Step -6: Apply identity law
≡q∨r [∵(T∧a)≡q]
Hence, (p∧q)∨(∼p∧q)∨(∼q∧r)≡q∨r
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