Subset meaning in sets explained

Learn and know the meaning of subset in the set theory chapter which is very important to know by every student. In subsets we have two types i.e. proper subset and improper subsets, these two meanings also we will know now.

Subset meaning in sets explained

Clear cut explanation is given about subset meaning i.e. definition and also example. Along with subset I gave definitions of proper subset and improper subset with examples in a simple language. Just go through that I hope you can understand easily.

Subset meaning (definition) as follows:

If all the elements of set P are present in set Q then we say that set P is subset of set Q. we can say the same statement in another form also. The another definition of subset is “if all the elements of the set P are also the elements of set Q then we say that set P is subset of set Q”. we can represent it as P ⊆ Q.

Example:

P = {2, 8, 14, 27, 39} and Q= {3, 5, 2, 7, 8, 11, 14, 19, 25, 27, 33, 45, 39, 74}

We observe that all the elements of set P are present in set Q, so we say that set P is the subset of set Q.

Proper subset meaning (definition) as follows:

If set H is the subset of set K and set H is not equal to set K (set H ≠ set K) then we say that set H is the proper subset of set K. we can represent it as H ⊂ K.

Example:

H = {a, h, n,v,c} and K ={f,l,a,x,h,o,n,v,s,c}

By observing the two sets, we can say that all the elements of set H are also the elements of set K and set H ≠ set K. so H ⊂ K.

Improper subset meaning (definition) as follows:

If set H is the subset of set K and set H is equal to set K (set H = set K) then we say that set H is the improper subset of set K.

Example:

H= {1, 4, 6, 8, 7} and K = {6, 1, 4, 8, 7}

By observing the two sets, we can say that all the elements of set H are also the elements of set K and set H = set K. so we say set H is the improper subset of set K.

Finally, I hope that you have understood everything about subset i.e. subset meaning, definition, examples and types of subsets.

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