Question

The total number of proper subsets for {a, b, c, d} are?

• A. $17$
• B. $7$
• C. $15$
• D. $20$

Answer 1

Answer: (C)

$15$

We have to find the total number of proper subsets for $\{a,b,c,d\}$
We know that, "A proper subset of a set $A$ is a subset $B\subset A$ but $B\ne A$".
That is the number of proper subsets in a set having $n$ items is $2^n-1$.
Consider $\{a,b,c,d\}$.
There are $4$ elements in the above set.
$\Rightarrow$ Total number of proper subsets are $2^4-1=16-1=15$.
Therefore the total number of proper subsets for $\{a,b,c,d\}$ is $15$.