\displaystyle \textbf{Question 1. }\text{If }A=\{1,2,4\},\ B=\{2,4,5\}\text{ and }C=\{2,5\}, \\ \text{ write }(A-C)\times(B-C).
\displaystyle \text{Answer:}
\displaystyle A-C=\{1,4\}
\displaystyle B-C=\{4\}
\displaystyle (A-C)\times(B-C)=\{(1,4),(4,4)\}
\\

\displaystyle \textbf{Question 2. }\text{If }n(A)=3,\ n(B)=4,\text{ then write }n(A\times A\times B).
\displaystyle \text{Answer:}
\displaystyle n(A\times A\times B)=n(A)\cdot n(A)\cdot n(B)
\displaystyle =3\times3\times4=36
\\

\displaystyle \textbf{Question 3. }\text{If }R\text{ is a relation defined on the set } Z\text{ of integers by the rule } \\ (x,y)\in R\Leftrightarrow x^2+y^2=9,\text{ then write domain of }R.
\displaystyle \text{Answer:}
\displaystyle x^2+y^2=9
\displaystyle \text{Possible integer values of }x\text{ are }-3,0,3
\displaystyle \therefore \text{Domain of }R=\{-3,0,3\}
\\

\displaystyle \textbf{Question 4. }\text{If }R=\{(x,y):x,y\in Z,\ x^2+y^2\leq4\}\text{ is a relation defined on the set } \\ Z\text{ of integers, then write domain of }R.
\displaystyle \text{Answer:}
\displaystyle x^2+y^2\leq4
\displaystyle \text{Possible integer values of }x\text{ are }-2,-1,0,1,2
\displaystyle \therefore \text{Domain of }R=\{-2,-1,0,1,2\}
\\

\displaystyle \textbf{Question 5. }\text{If }R\text{ is a relation from set }A=\{11,12,13\}\text{ to set }B=\{8,10,12\} \\ \text{ defined by }y=x-3,\text{ then write }R^{-1}.
\displaystyle \text{Answer:}
\displaystyle R=\{(11,8),(13,10)\}
\displaystyle \therefore R^{-1}=\{(8,11),(10,13)\}
\\

\displaystyle \textbf{Question 6. }\text{Let }A=\{1,2,3\}\text{ and }R=\{(a,b):|a^2-b^2|\leq5,\ a,b\in A\}.\text{ Then write }R\text{ as set of ordered pairs.}
\displaystyle \text{Answer:}
\displaystyle R=\{(1,1),(1,2),(2,1),(2,2),(2,3),(3,2),(3,3)\}
\\

\displaystyle \textbf{Question 7. }\text{Let }R=\{(x,y):x,y\in Z,\ y=2x-4\}.\text{ If }(a,-2)\text{ and } \\ (4,b^2)\in R,\text{ then write the values of }a\text{ and }b.
\displaystyle \text{Answer:}
\displaystyle -2=2a-4
\displaystyle 2a=2
\displaystyle a=1
\displaystyle b^2=2(4)-4=4
\displaystyle b=\pm2
\\

\displaystyle \textbf{Question 8. }\text{If }R=\{(2,1),(4,7),(1,-2),\ldots\},\text{ then write the linear relation between} \\ \text{the components of the ordered pairs of the relation }R.
\displaystyle \text{Answer:}
\displaystyle \text{Let relation be }y=ax+b
\displaystyle (2,1)\Rightarrow2a+b=1
\displaystyle (4,7)\Rightarrow4a+b=7
\displaystyle 2a=6\Rightarrow a=3
\displaystyle b=1-6=-5
\displaystyle \therefore y=3x-5
\\

\displaystyle \textbf{Question 9. }\text{If }A=\{1,3,5\}\text{ and }B=\{2,4\},\text{ list the elements of }R,\text{ if } \\ R=\{(x,y):x,y\in A\times B\text{ and }x>y\}.
\displaystyle \text{Answer:}
\displaystyle R=\{(3,2),(5,2),(5,4)\}
\\

\displaystyle \textbf{Question 10. }\text{If }R=\{(x,y):x,y\in W,\ 2x+y=8\},\text{ then write the domain and range of }R.
\displaystyle \text{Answer:}
\displaystyle 2x+y=8
\displaystyle \text{Possible ordered pairs are }(0,8),(1,6),(2,4),(3,2),(4,0)
\displaystyle \text{Domain}=\{0,1,2,3,4\}
\displaystyle \text{Range}=\{0,2,4,6,8\}
\\

\displaystyle \textbf{Question 11. }\text{Let }A\text{ and }B\text{ be two sets such that }n(A)=3\text{ and }n(B)=2. \\ \text{ If }(x,1),(y,2),(z,1)\text{ are in }A\times B,\text{ write }A\text{ and }B.
\displaystyle \text{Answer:}
\displaystyle A=\{x,y,z\}
\displaystyle B=\{1,2\}
\\

\displaystyle \textbf{Question 12. }\text{Let }A=\{1,2,3,5\},\ B=\{4,6,9\}\text{ and }R\text{ be a relation from }A\text{ to }B \\ \text{ defined by }R=\{(x,y):x-y\text{ is odd}\}. \text{Write }R\text{ in roster form.}
\displaystyle \text{Answer:}
\displaystyle R=\{(1,4),(1,6),(2,9),(3,4),(3,6),(5,4),(5,6)\}

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