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Maths
Sets
Using the Venn diagram shows that $(A - B)$,$(A \cap B)$ and $(B - A)$ are disjoint sets, taking $A = \left\{ {2,4,6,8,10,\left. {12} \right\}} \right.$and $B = \left\{ {3,6,9,12,\left. {15} \right\}} \right.$
Maths
Sets
In a class of $120$ students, $30$ study Maths, $40$ study Physics, $45$ study Chemistry, $15$ study Math and Physics, $20$ study Physics and Chemistry, $12$ study Math and Chemistry and $8$ study all the three. How many are
a.Studying at least one of these subjects
b.did not study any of these
c.how many take only one subject
d.how many study exactly $2$ of the three subjects
Maths
Sets
If $A$ is any set, then
A) $A \cup A^{\prime} = \phi$
B) $A \cup A^{\prime} = U$
C) $A \cap A^{\prime} = U$
D) None of the above
Maths
Sets
If $A \subset B$ then show that $A \cap B = {\rm A}$ (Use Venn Diagram).
Maths
Sets
If $M \cup N = N \cup R$ and $M \cap N = N \cap R$ then which of the following is necessarily true?
A. $M = N$
B. $N = R$
C. $M = R$
D. $M = N = R$

Maths
Sets
In order that a relation defined on a non- empty set A is an equivalence relation, it is sufficient, if R
1. Is reflexive
2. Is symmetric
3. Is transitive
4. Possesses all the above properties

Maths
Sets
Which of the following sets are equal?
(i) $A = \{ 1,2,3,4\}$, $B = \{ 4,3,2,1\}$
(ii) $A = \{ 4,8,12,16\}$, $B = \{ 8,4,16,18\}$
(iii) $X = \{ 2,4,6,8\}$ ,$Y = \ \{\ x:x\ \text{is a positive even integer} \ 0 < x < 10\ \}$
(iv) $P = \ \{\ x:x\ \text{is a multiple of}\ 10,\ x \in N\ \}$ , $Q = \{ 10,15,20,25,30,\ldots\}$
Maths
Sets
Is the Set of odd numbers between $7$ and $19$ an empty set?
Maths
Sets
If $X = \left\{ {a,\left\{ {b,c} \right\},d} \right\}$, which of the following is a subset of $X$ $?$
A. $\left\{ {a,b} \right\}$
B. $\left\{ {b,c} \right\}$
C. $\left\{ {c,d} \right\}$
D. $\left\{ {a,d} \right\}$

Mathematics
Sets
Let $A = \left\{ {1,2,3} \right\}$ and $B = \left\{ {2,3,4} \right\}$ , then which of the following relations is a function from A to B?
A $\left\{ {\left( {1,2} \right),\left( {2,3} \right),\left( {3,4} \right),\left( {2,2} \right)} \right\}$
B $\left\{ {\left( {1,2} \right),\left( {2,3} \right),\left( {1,3} \right)} \right\}$
C $\left\{ {\left( {1,3} \right),\left( {2,3} \right),\left( {3,3} \right)} \right\}$
D $\left\{ {\left( {1,1} \right),\left( {2,3} \right),\left( {3,4} \right)} \right\}$

Mathematics
Sets
Let S = {1, 2, 3, 4}. The total number of unordered pairs of disjoint subsets of S equal to,
$\left( a \right)$ 25
$\left( b \right)$ 34
$\left( c \right)$ 42
$\left( d \right)$ 41
Mathematics
Sets
Find the union of each of the following pairs of sets:
(i) $X = \{ 1,3,5\} Y = \{ 1,2,3\}$
(ii)$A = \{ a,e,i,o,u\} ,B = \{ a,b,c\}$
(iii)$A = \{ x:x$ is a natural number and multiple of $3\}$
$B = \{ x:x$is a natural number less than $6\}$
(iv)$A = \{ x:x$ is a natural number and $1 < x \leqslant 6\}$
$B = \{ x:x$is a natural number and $6 < x < 10\}$
(v) $A = \{ 1,2,3\} ,B = \phi$

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