Consider the following three statements:
$(A)$ If $3+3=7$ then $4+3=8$.
$(B)$ If $5+3=8$ then earth is flat.
$(C)$ If both $(A)$ and $(B)$ are true then $5+6=17$.
Which of the following statements is correct?

  • A
    $(A)$ and $(C)$ are true while $(B)$ is false
  • B
    $(A)$ is true while $(B)$ and $(C)$ are false
  • C
    $(A)$ is false,but $(B)$ and $(C)$ are true
  • D
    $(A)$ and $(B)$ are false while $(C)$ is true

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The logical statement $(p \wedge \sim q) \vee q \vee (\sim p \wedge q)$ is equivalent to

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$p$: If voltage increases, then current decreases.
$q$: If voltage does not increase, then current does not decrease.
$r$: If current decreases, then voltage increases.
$s$: If current does not decrease, then voltage does not increase.
Which of the following pairs of statements have the same meaning?

Write the negation of the following statement:
The number $2$ is greater than $7.$

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$s:$ There exists a number $x$ such that $0 < x < 1.$

If $p, q, r$ are simple propositions,then $(p \wedge q) \wedge (q \wedge r)$ is true,then:

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