Question

Let A = {2, 3, 4, 5, 6, 7} B = {2, 4, 7, 8) C = {2, 4} ,then which of the following statements are True?
(a) B $\subset$ A
(b) C $\subset$ A
(c) B $\subseteq$ C
(d) C $\subset$ B

• A. Both (a) and (d)
• B. Both (b) and (d)
• C. only (d)
• D. only (b)

Answer 1

Answer: (B)

Both (b) and (d)

Given $A=\{2,3,4,5,6,7\},B=\{2,4,7,8\},C=\{2,4\}$
Let us find which of the following statements are true.
$\left(a\right)$ Consider $B\subset A$
Since $8\notin A,B⊈A$
Therefore the statement "$B\subset A$" is not true.
$\left(b\right)$ Consider $C\subset A$
Since $2,4\in A,C\subset A$
Therefore the statement "$C\subset A$" is true.
$\left(c\right)$ Consider $B\subseteq C$
Since $7,8\notin C,B⊈C$
Therefore the statement "$B\subseteq C$" is not true.
$\left(d\right)$ Consider $C\subset B$
Since $2,4\in B,C\subset B$
Therefore the statement "$C\subset B$" is true.
Thus both $\left(b\right)$ and $\left(d\right)$ are true.