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Difference of set - (Concept)
The difference between the sets $A$ and $B$ in this order is the set of elements that belong to $A$ but not to B .
Symbolically, we write A - B and read as "A minus B".
For example, If $A=\{1,2,3,4\}$ and $B=\{4,5,6,8\}$,
Then, $A-B=\{1,2,3\}$ and $B-A=\{5,6,8\}$
The sets $A-B, A \cap B$ and $B-A$ are mutually disjoint sets, i.e., the intersection of any two of these sets is the null set as shown in figured
Properties of Difference of Sets
1. In general $A$ - $B$ does not equal $B$ - $A$
2. $\mathrm{A}-\mathrm{A}=\phi$
3. $\mathrm{A}-\phi=\mathrm{A}$
4. $\mathrm{A}-\mathrm{U}=\phi$
5. If $A$ is a subset of $B$, then $A-B=\phi$
Symmetric Difference of Sets ( $A \Delta B$ )
The symmetric difference of two sets $A$ and $B$ is defined as
$
A \Delta B=(A-B) \cup(B-A)
$
Venn Diagram
Clearly, A Δ B also equals ( A ∪ B) - ( A ∩ B )
| Exam | Chapter |
| JEE MAIN | Sets, Relations and Functions |
Let $\mathrm{A}, \mathrm{B}$ and C be sets such that $\phi \neq A \cap B \subseteq C$. Then which of the following statements is not true?
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If and
; then:
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If A, B, and C are any three sets, then $A-(B\cup C)$ is equal to?
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If A, B and C are non-empty sets, then
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Let and
, then the sum of all the elements of the set
is equal to__________
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If $A, B, C$ are non-empty sets, then $(A-B) U(B-A)$ equals
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Which of the set representation depicts the shaded region?
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If then
is invertiable in the domain.
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Let and let
. then the number of values of
such that
for infinitely many real number
is.
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$If A\subset B,then\: A-B=$
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$A=\{1,2,3,5,9,11\}$ and $B=\{-1,-2,3,9\}$, Then $A-B=$
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If $\mathrm{A= \left \{ x:\, x= 2n,\, n\leq 5,n\in N \right \}\, and\; B= \left \{ x:\, x= 3n,n\leq 4,n\in N \right \},then\; A-\left ( A-B \right )\: equals}$
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If $f=\{(1,2),(2,3),(3,9)\}$ has domain $A$, range $B$.If co-domain is $C=\{1,2,3,4,9\}$,then $(A \cap B)-C$ equals
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If U = {1,2,3,4,5} and A' = {2,3,4} and B' = {1,2,3}, then B - A equals
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Let $S=\{4,6,9\}$ and $T=\{9,10,11, \ldots, 1000\}_{\text {. If }}$
$\mathrm{A}=\left\{\mathrm{a}_1+\mathrm{a}_2+\ldots+\mathrm{a}_{\mathrm{k}}: \mathrm{k} \in \mathbf{N}, \mathrm{a}_1, \mathrm{a}_2, \mathrm{a}_3, \ldots, \mathrm{a}_{\mathrm{k}} \in \mathrm{S}\right\}$, then the sum of all the elements in the set $\mathrm{T}-\mathrm{A}$ is equal to $\qquad$
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The difference of the sets A and B in this order is the set of elements which belong to A but not to B. Symbolically, we write A – B and read as
“ A minus B”.
