Which of the following is not logically equivalent to the proposition : “A real number is either rational or irrational”.
Which of the following is not logically equivalent to the proposition : “A real number is either rational or irrational”.
- A
If a number is neither rational nor irrational then it is not real
- B
If a number is not a rational or not an irrational, then it is not real
- C
If a number is not real, then it is neither rational nor irrational
- D
If a number is real, then it is rational or irrational
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Let $p$ and $q $ stand for the statement $"2 × 4 = 8" $ and $"4$ divides $7"$ respectively. Then the truth value of following biconditional statements
$(i)$ $p \leftrightarrow q$
$(ii)$ $~ p \leftrightarrow q$
$(iii)$ $~ q \leftrightarrow p$
$(iv)$ $~ p \leftrightarrow ~ q$
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$(i)$ $p \leftrightarrow q$
$(ii)$ $~ p \leftrightarrow q$
$(iii)$ $~ q \leftrightarrow p$
$(iv)$ $~ p \leftrightarrow ~ q$