Question

I need the answer with a fair explanation.

Answer 1

Answer:

C=> {1,2,3}

Step-by-step explanation:

because {1,2,3} is a common number that's why it was repeated.

Answer 2

Answer:

14

Step-by-step explanation:

For A ⊂ C ⊂ B, All elements of set A will be a part of set C but set C will have at least 1 element from set B (except 1,2,3 as they r already included) so that A ≠ C but not more than 3 elements as if we choose all 4 then B = C but we want C ⊂ B.

As we need to select at least 1 element from Set B but only from {4,5,6,7} there can be 4 cases for it.

We will calculate it using Permutation & Combinations,

•) SELECTING 1 ELEMENT FROM {4,5,6,7}.

=> we need to select 1 from 4 hence,

=> $^4C_1$

=> $\frac {4!}{3!*1!}$

=> 4 selections possible ----------(1)

•) SELECTING 2 ELEMENTS FROM {4,5,6,7}.

=> we need to select 2 from 4 hence,

=> $^4C_2$

=> $\frac {4!}{2!*2!}$

=> 6 selections possible ----------(2)

•) SELECTING 3 ELEMENTS FROM {4,5,6,7}.

=> we need to select 3 from 4 hence,

=> $^4C_3$

=> $\frac {4!}{3!*1!}$

=> 4 selections possible ----------(3)

Add (1), (2), (3).

we get, at most 14 possible subsets.

HOPE IT HELPS!!!