# Let \[A = \left\{ {3,6,12,15,18,21} \right\},{\text{ }}B = \left\{ {4,8,12,16,20} \right\},{\text{ }}C = \left\{ {2,4,6,8,10,12,14,16} \right\}\]

and \[D = \left\{ {5,10,15,20} \right\}\]. Find A – C.

Last updated date: 21st Mar 2023

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Answer

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Hint: No use of set B and D.

As, we know that if X and Y are two sets then,

\[X - Y\]will be a set, which includes all the elements of X excluding the elements

that are also present in Y.

So, here we had to find the value of A – C.

So, A – C will be a set which have all elements that belongs to A excluding elements

That also belongs to C.

So, A - C\[ = \left\{ {3,6,12,15,18,21} \right\} - \left\{ {2,4,6,8,10,12,14,16} \right\}\]

Hence, A - C\[ = \left\{ {3,15,18,21} \right\}\]

Note:- Whenever we came up with this type of problem then we should first draw

Venn’s Diagram as this will be the efficient way to solve the problems involving sets.

And then remember that if X and Y are then \[X - Y\]will be a set, which includes all the

elements of X excluding the elements that are also present in Y.

As, we know that if X and Y are two sets then,

\[X - Y\]will be a set, which includes all the elements of X excluding the elements

that are also present in Y.

So, here we had to find the value of A – C.

So, A – C will be a set which have all elements that belongs to A excluding elements

That also belongs to C.

So, A - C\[ = \left\{ {3,6,12,15,18,21} \right\} - \left\{ {2,4,6,8,10,12,14,16} \right\}\]

Hence, A - C\[ = \left\{ {3,15,18,21} \right\}\]

Note:- Whenever we came up with this type of problem then we should first draw

Venn’s Diagram as this will be the efficient way to solve the problems involving sets.

And then remember that if X and Y are then \[X - Y\]will be a set, which includes all the

elements of X excluding the elements that are also present in Y.

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