List of top Mathematics Questions on Set Theory asked in KEAM

The number of positive integers up to 100, which are divisible by 3 or 7 but not by both 3 and 7, is

Let $X=\{1,2,3,4,5,6,7}$. Let $R=\{(1,1), (1, 2), (1, 3), (5, 6), (6, 7), (7,5)\}$ be a relation on $X$. Then the relation $R$ will become reflexive if we include the pairs

Let $X=\{a,b,c,d,e}$ and $A=\{a,b,c,d\}$. Let $P=\{B:B\subseteq X \text{ and } A\setminus B=\{d\}\}$. Then the number of elements in the set $P$ is

Given the following information: \[ n(A \times B) = 160, \quad n(B \times C) = 80, \quad n(A \times C) = 240 \] Find \( n(A) \).

If $ n(A) = 7 $ and the number of relations from A to B is 128. Then find } $ n(B) $.

If the operation $\oplus$ is defined by $a \oplus b = a^2 + b^2$ for all real numbers $a$ and $b$, then $(2 \oplus 3) \oplus 4 =$

If the operation $\oplus$ is defined by $a \oplus b = a^2 + b^2$ for all real numbers $a$ and $b$, then $(2 \oplus 3) \oplus 4 =$

If the operation $\oplus$ is defined by $a \oplus b = a^2 + b^2$ for all real numbers $a$ and $b$, then $(2 \oplus 3) \oplus 4 =$