Question

If A = { a , b, c, d, e}, B = { c, d, e, f }, C = {b, d}, D = { a , e}

then which of the following statements are true and which are false ?

( i ) C $\subseteq$ B ( ii ) A $\subseteq$ D ( iii ) D $\subseteq$B ( iv ) D$\subseteq$A ( v ) B $\subseteq$A (vi) C $\subseteq$A

Answer 1

We have, A = {a , b, c, d, e}, B = {c, d, e, f }, C = {b, d}, D = {a, e}

(i) Since, $b\in C\mathrm{but}b\notin B$

So, C $\subseteq$ B is false.

(ii) Since, $b\in A\mathrm{but}b\notin D$

So, A $\subseteq$ D is false.

(iii) Since, $a\in D\mathrm{but}a\notin B$

So, D $\subseteq$ B is false.

(iv) Since, all elements of set D is in set A.

So, D $\subseteq$ A is true.

(v) Since, $f\in B\mathrm{but}f\notin A$

So, B $\subseteq$ A is false.

(vi) Since, all elements of set C is in set A.

So, C $\subseteq$ A