let A= {1,2,3,4}, B={1,2,3}, C={2,4}. Find all sets X satisfying each pair of conditions:

i) X ⊂ B and X ⊄ C       ii) X⊂ B, X ≠ B and X  ⊄  C         iii)X ⊂ A, X⊂ B and X ⊂ C

plzzzz answer this question and explain further to... thanks! :)

Given, sets are A = {1, 2, 3, 4}

 B = {1, 2, 3}

 C = {2, 4}

Subsets of A are:

Φ, {1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}, {1, 2, 3}, {1, 2, 4}, {2, 3, 4}, {1, 3, 4}, {1, 2, 3, 4}

Subsets of B are:

Φ, {1}, {2}, {3}, {1, 2}, {2, 3}, {1, 3}, {1, 2, 3}

Subsets of C are: Φ, {2}, {4}, {2, 4}

∴ All subsets are:

Φ, {1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}, {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4},{1, 2, 3, 4}.

Now, 

(1) The sets X  which satisfies the condition X ⊂ B where B = {1, 2, 3} are

Φ, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}

[Mind that {1, 2, 3} {1, 2, 3} as 'C' is a notation for proper containment]

and X C where C = {2, 4} are:

{1}, {3}, {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}, {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4},{1, 2, 3, 4}.

[only Φ, {2}, {4} are properly contained in C = {2, 4}]

Other parts can be solved in the same way. If you face any difficulty, then please do get back to us.