Question

Let d = {b, a, c, k}, e = {t, a, s, k}, and f = {b, a, t, h}.

a) Set e is a subset of set d.
b) Set d is a subset of set f.
c) Set f is a subset of set e.
d) Set f is a subset of set d.

Answer 1

Set e is not a subset of set d. Set d is a subset of set f. Set f is not a subset of set e. Set f is not a subset of set d.

Step-by-step explanation:

To determine if set e is a subset of set d, we need to check if all elements of e are also in d.

d = {b, a, c, k}

e = {t, a, s, k}

As we can see, not all elements of e are in d; specifically, 't' and 's' are not in d. Therefore, e is not a subset of d.

For part b, set d is a subset of set f if all elements of d are also in f. In this case, 'b', 'a', and 'k' are all in f, so set d is a subset of set f.

For parts c and d, the same comparison can be made. Since set f does not contain all elements of set e, f is not a subset of e, and f is also not a subset of d.