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.

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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