Question

If U = {1, 3, 5, 7, 9, 11, 13}, then which of the following are subsets of U.
B = {2, 4}
A = {0}
C = {1, 9, 5, 13}
D = {5, 11, 1}
E = {13, 7, 9, 11, 5, 3, 1}
F = {2, 3, 4, 5}
a)A and B
b)C, D and E
c)A and D
d)Only A

Answer 1

HINT:-Before solving this question, we must know about
SETS AND SUB – SETS: A set is a well-defined collection of objects.
Two sets are equal if they have exactly the same elements in them.
A set that contains no elements is called a null set or an empty set.
If every element in ‘Set A’ is also in ‘Set B’, then Set A is a subset of Set B.

Complete step-by-step answer:
Let us now solve this question.

We shall consider every set.

U = {1, 3, 5, 7, 9, 11, 13}

• 1) B = {2, 4}

Let us check whether set B contains numbers that set U contains.

We can see that set B contains 2 and 4, which is not present in set U.

So, set B cannot be a subset of set U.

2) A = {0}

Let us check whether set A contains numbers that set U contains.

We can see that set A contains 0, which is not present in set U.

So, set A cannot be a subset of set U.

3) C = {1, 9, 5, 13}

Let us check whether set C contains numbers that set U contains.

We can see that set C contains 1, 9, 5, and 13, which is present in set U.

So, set C is a subset of set U.

4) D = {5, 11, 1}

Let us check whether set D contains numbers that set U contains.

We can see that set C contains 5, 11 and 1, which is present in set U.

So, set D is a subset of set U.

5) E = {13, 7, 9, 11, 5, 3, 1}

Let us check whether set E contains numbers that set U contains.

We can see that set E contains 13, 7, 9, 11, 5, 3 and 1, which is present in set U.

So, set E is a subset of set U.

6) F = {2, 3, 4, 5}

Let us check whether set F contains numbers that set U contains.

We can see that set F contains 2, 3, 4, and 5, which is not present in set U.

So, set F is not a subset of set U.

So, after considering the sets, we can say that only set C, set D and set E are the subsets of
the set U.

The only option that matches with the above explanation is (b) C, D, and E.




NOTE:-
Let us now know more about sets.

Sets, in mathematics, are an organized collection of objects and are usually represented in curly brackets {}, for example, A = {1,2,3,4} is a set.

One must do all the calculations in this question very carefully.

Also not only in this question, the students must be very careful while solving any such questions as if there is any mistake in the calculus, then the answer can come out to be wrong.