Operations on Set | 9th Math Chapter 3 Lecture 3
Operations on Set is a topic of 9th Math Chapter 3. In this lecture we will check union of sets, intersection of sets, difference of sets, disjoint sets, overlapping sets and complement of a set.
Union of two set:-
Union of two sets A and B is the set of all the element which belong two A or B or both.
In Set builder notation
$$A\cup B=\{x\vert x\in A\vee x\in B\vee x\in A\wedge B\}$$
Example:-
A = {1,2} B = {2,3,4} AUB = { 1,2,3,4 }
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Intersection of two sets:-
Intersection of two sets A and B is the set of all the element which belong to both A and B.
In Set builder notation
$$A\cap B=\;\{\;x\;\vert\;x\in A\;\wedge\;x\in B\;\}$$
Example:-
$$A=\{1,2\}\;\;B=\{2,3,4\}\;\;A\cap B=\{2\}$$
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Difference of two sets:-
It there are two sets A and B, difference of A to B denoted A-B consists of all the elements belong to A but does not belong to B.
$$A-B\;=\;\{\;x\;\vert\;x\in A\wedge x\not\in B\;\}$$
$$B-A\;=\;\{\;x\;\vert\;x\in B\wedge x\not\in A\;\}$$
Example:-
A = {1,2} B = {2,3,4} A-B = {1} B-A = { 3,4 }
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Disjoint sets:-
If the intersection of two set is the empty, the sets are called disjoint sets.
A = { 1 , 2 } , B = { 3 , 4 }
$$A\cap B\;=\;\{\;\;\}$$
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Overlapping Sets:-
If the intersection of two sets is non-empty but neither is a subset of the other.
A = { 1 , 2 } B = { 2 , 3 }
$$A\cap B\;=\;\{\;2\;\}$$
Also, A is not subset of B and B is not subset of A
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Compliment of a set:-
Compliment of set A is the set of all the element of U, which does not belong to A denoted by $$A^{c\;}\;or\;\;A’$$.
$$A^{c\;}=\;\{x\;\vert\;x\;\in\cup\wedge x\not\in A\}$$
U = { 1 , 2 , 3 , 4 , 5 }
A = { 1 , 2 , 3 }
$$A^c\;=\;\{\;4\;,\;5\;\}$$
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Check! Some important links below
You tube Channel 9th class Sir Najam
MCQs 9th Math chapter 2 2025
Home page Notespunjab.com
