Let $A = \{a, b, c\}, B = \{b, c, d\}, C = \{a, b, d, e\}$. Then $A \cap (B \cup C)$ is

In an examination,$30 \%$ of the total students failed in Hindi,$45 \%$ failed in English,and $20 \%$ failed in both the subjects. Find the percentage of those who passed in both the subjects. (in $\%$)

Let $A, B, C$ be three sets such that $n(A \cap B) = n(B \cap C) = n(C \cap A) = n(A \cap B \cap C) = 2$. Then $n((A \times B) \cap (B \times C))$ is equal to -

Consider the two sets:
$A = \{m \in R : \text{both the roots of } x^{2} - (m+1)x + m+4 = 0 \text{ are real}\}$ and $B = [-3, 5)$.
Which of the following is not true?

If $A = \{a, b\}$,$B = \{c, d\}$,$C = \{d, e\}$,then the set $\{(a, c), (a, d), (a, e), (b, c), (b, d), (b, e)\}$ is equal to:

Let $n(U) = 700, n(A) = 200, n(B) = 300$ and $n(A \cap B) = 100,$ then $n(A^c \cap B^c) = $