Question

Let C ,A be subsets of a set. Prove that ,B A ∩ B ⊆ C iff A ⊆ B complement ∪ C.

Answer 1

Let A={1,2,3}

B={1,2,3,4,5}

$B'=$ {$\phi$ }

And C={1,2,3,6,7}

So, As per the question, and as per the given set, $A\subseteq C$

Now, $A\cap B=$ {1,2,3}$--------(i)$

From the equation (i) and set C,

$A\cap B\subseteq C$

It is possible because

$B'\cup C=$ {1,2,3,6,7}$---------(ii)$

From the equation (ii) and the set A, we can see that A is the subset of the equation (ii)

Hence proved.