Educational

Find the Domain and Range of R = {(x, y) : 2x + y = 8} Find the Domain and Range of R = {(x, y) : 2x + y = 8} Question If \[ R=\{(x,y): x,y\in W,\ 2x+y=8\}, \] then write the domain and range of \( R \). Solution Given, \[ 2x+y=8 \] […]

List the Elements of R if R = {(x, y) : x > y} for A = {1, 3, 5} and B = {2, 4}

Find the Linear Relation Between the Components of Ordered Pairs of R Find the Linear Relation Between the Components of Ordered Pairs of R Question If \[ R=\{(2,1),(4,7),(1,-2),\ldots\}, \] then write the linear relation between the components of the ordered pairs of the relation \( R \). Solution Let the linear relation be \[ y=ax+b

Find the Values of a and b if (a, −2) and (4, b²) ∈ R Find the Values of a and b if (a, −2) and (4, b²) ∈ R Question Let \[ R=\{(x,y): x,y\in Z,\ y=2x-4\} \] If \[ (a,-2)\in R \] and \[ (4,b^2)\in R, \] then write the values of \( a

Write R as a Set of Ordered Pairs for |a² − b²| ≤ 5 Write R as a Set of Ordered Pairs for |a² − b²| ≤ 5 Question Let \[ A=\{1,2,3\} \] and \[ R=\{(a,b): |a^2-b^2|\le5,\ a,b\in A\} \] Then write \( R \) as a set of ordered pairs. Solution \[ |1^2-1^2|=0\le5 \]

Find R⁻¹ if R is Defined by y = x − 3 Find R⁻¹ if R is Defined by y = x − 3 Question If \( R \) is a relation from set \[ A=\{11,12,13\} \] to set \[ B=\{8,10,12\} \] defined by \[ y=x-3, \] then write \( R^{-1} \). Solution Given, \[

Find the Domain of Relation R Where x² + y² ≤ 4 Find the Domain of Relation R Where x² + y² ≤ 4 Question If \[ R=\{(x,y): x,y\in Z,\ x^2+y^2\le4\} \] is a relation defined on the set \( Z \) of integers, then write domain of \( R \). Solution Given, \[ x^2+y^2\le4

Find the Domain of Relation R Where x² + y² = 9 Find the Domain of Relation R Where x² + y² = 9 Question If \( R \) is a relation defined on the set \( Z \) of integers by the rule \[ (x,y)\in R \iff x^2+y^2=9, \] then write domain of \(

If n(A) = 3 and n(B) = 4, Find n(A × A × B) If n(A) = 3 and n(B) = 4, Find n(A × A × B) Question If \[ n(A)=3,\quad n(B)=4, \] then write \[ n(A\times A\times B) \] Solution \[ n(A\times A\times B)=n(A)\times n(A)\times n(B) \] \[ =3\times3\times4 \] \[ =36 \]

Find (A − C) × (B − C) for A = {1, 2, 4}, B = {2, 4, 5} and C = {2, 5} Find (A − C) × (B − C) for A = {1, 2, 4}, B = {2, 4, 5} and C = {2, 5} Question If \[ A=\{1,2,4\},\ B=\{2,4,5\}\ \text{and}\ C=\{2,5\},