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Question

Which of the following predicate calculus statements is/are valid

A
(x)P(x)(x)Q(x)(x){P(x)Q(x)}
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B
(x)P(x)(x)Q(x)(x){P(x)Q(x)}
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C
(x){P(x)Q(x)}(x)P(x)(x)Q(x)
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D
(x){P(x)Q(x)}(x)P(x)xQ(x)
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Solution

The correct option is A (x)P(x)(x)Q(x)(x){P(x)Q(x)}
According to distributive properties
x(P(x)Q(x))xP(x)xQ(x)

x(P(x)Q(x)x(P(x)Q(x))

x(P(x)Q(x))xP(x)xQ(x)

x(P(x)Q(x))xP(x)xQ(x)
So option (a) is valid.

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