List of top Mathematics Questions on implications

Find \(\int_{0}^{\frac{\pi}{2}} \sqrt{\cos x \sin 2x} \, dx\)
\( \sim [(\sim p) \wedge q] \) is logically equivalent to:
\( \sim [(\sim p) \wedge q] \) is logically equivalent to:
\( \sim [(\sim p) \wedge q] \) is logically equivalent to:
\(a,b,c\) are prime numbers, \(x\) is an even number, \(y\) is an odd number. Which of the following is/are never true? I. \(a + x = b\) II. \(b + y = c\) III. \(ab = c\) IV. \(a + b = c\)
The inverse of the proportion \( (p \wedge q) \Rightarrow r \) is