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The truth value of the statements:

$\exists ! xP(x) \rightarrow \exists xP(x) \text{ and } \exists ! x \rceil P(x) \rightarrow \rceil \forall xP(x)$, (where the notation $\exists ! x P(x)$ denotes the proposition “There exists a unique $x$ such that $P(x)$ is true”) are:

  1. True and False
  2. False and True
  3. False and False
  4. True and True
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Answer D

S1: If there exists a unique value, x, that makes P(x) true, then obviously exists an x value for which P(x) is true

S2: If there is a unique value, x, that makes P(x) false, then definitely there a value, x, that can make P(x) false

Hence, both the statements are correct
Answer:

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