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Question

For a given pair of sets, identify the pair where the first set is the subset of the second set.

A
{p,q,r} & {a,p,b,q,c,r}
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B
{x:x is an isoceles triangle in xy plane} & {y:y is a triangle in xy plane}
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C
{m:m is a multiple of 10} & {n:n is a multiple of 5}
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D
{b:b is a vowel in the word TEA} & {c:c is a vowel in the word CAT}
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Solution

The correct option is C {m:m is a multiple of 10} & {n:n is a multiple of 5}
A set is a subset of another set if each and every element of the set is an element of the second set.
Using this let's take the examples one by one.
A.{p,q,r} & {a,p,b,q,c,r}
Here, the first set has elements p,q,r which are also the elements of the second set.
This means the first set is a subset of the second set.

B.{x:x is an isoceles triangle in xy plane} & {y:y is a triangle in xy plane}
Here, the first set contains all isoceles triangles in the xy plane.
And the second set contains all triangles in the xy plane.
Clearly, this means the first set is the subset of the second set.

C.{m:m is a multiple of 10} & {n:n is a multiple of 5}
In roster form we can write the sets as:
{10,20,30,...} & {5,10,15,20,25,...}
Here, also all the elements of the first set will be an element of the second set.
This means first set will be the subset of the second set.

D.{b:b is a vowel in the word TEA} & {c:c is a vowel in the word CAT}
In roster form we can write the sets as:
{E,A} & {A}
Clearly, E{A}
This means the first set is not the subset of the second case.

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