The equivalent function of $\log {x^2}$ is

In a class of $140$ students numbered $1$ to $140$,all even-numbered students opted for the Mathematics course,those whose number is divisible by $3$ opted for the Physics course,and those whose number is divisible by $5$ opted for the Chemistry course. The number of students who did not opt for any of the three courses is:

Out of $800$ boys in a school,$224$ played cricket,$240$ played hockey,and $336$ played basketball. Of the total,$64$ played both basketball and hockey,$80$ played cricket and basketball,and $40$ played cricket and hockey; $24$ played all three games. The number of boys who did not play any game is:

In a town with a population of $5000$,$3200$ people are egg-eaters,$2500$ are meat-eaters,and $1500$ eat both egg and meat. How many are pure vegetarians?

Sets $A$ and $B$ have $3$ and $6$ elements respectively. What can be the minimum number of elements in $A \cup B$?

Let $A = \{1, 3, 5\}$ and $B = \{x : x \text{ is an odd natural number } < 6\}$. Which of the following is false?