If A = {-1, 1}, Find A×A×A If \(A=\{-1,1\}\), Find \(A\times A\times A\) Question If \[ A=\{-1,1\}, \] find \[ A\times A\times A. \] Solution Given: \[ A=\{-1,1\} \] The Cartesian product \[ A\times A\times A \] is the set of all ordered triples \((a,b,c)\) where \[ a,b,c \in A. \] Thus, all possible ordered […]

Let A = {1, 2, 3, 4} and R = {(a, b) : a Divides b}. Write R Explicitly Let \(A=\{1,2,3,4\}\) and \(R=\{(a,b): a \text{ divides } b\}\). Write \(R\) Explicitly Question Let \[ A=\{1,2,3,4\} \] and \[ R=\{(a,b): a\in A,\ b\in A,\ a \text{ divides } b\}. \] Write \(R\) explicitly. Solution Given: \[

If n(A)=3 and n(B)=2, Find Sets A and B from Ordered Pairs in A×B If \(n(A)=3\) and \(n(B)=2\), Find Sets \(A\) and \(B\) from Ordered Pairs in \(A\times B\) Question Let \(A\) and \(B\) be two sets such that \[ n(A)=3 \] and \[ n(B)=2. \] If \[ (x,1),\ (y,2),\ (z,1) \] are in \[

Show That A×B and B×A Have a Common Element iff A and B Have a Common Element Show That the Sets \(A\times B\) and \(B\times A\) Have an Element in Common iff the Sets \(A\) and \(B\) Have an Element in Common Question Let \(A\) and \(B\) be two sets. Show that the sets \[

If n(A)=5 and n(B)=4 with 3 Common Elements, Find n(A×B) and n{(A×B) ∩ (B×A)} If A and B Have 3 Common Elements, n(A)=5 and n(B)=4, Find \(n(A\times B)\) and \(n\{(A\times B)\cap(B\times A)\}\) Question If \(A\) and \(B\) are two sets having 3 elements in common, \[ n(A)=5 \] and \[ n(B)=4, \] find: \[ n(A\times

If A = {1, 2, 3} and B = {2, 4}, Find A×B, B×A, A×A×A, B×B and (A×B) ∩ (B×A) If \(A=\{1,2,3\}\) and \(B=\{2,4\}\), Find \(A\times B\), \(B\times A\), \(A\times A\times A\), \(B\times B\) and \((A\times B)\cap(B\times A)\) Question If \[ A=\{1,2,3\} \] and \[ B=\{2,4\}, \] find: \[ A\times B,\quad B\times A,\quad A\times A\times

Let A = {1, 2, 3} and B = {3, 4}. Find A×B and Show It Graphically Let \(A=\{1,2,3\}\) and \(B=\{3,4\}\). Find \(A\times B\) and Show It Graphically Question Let \[ A=\{1,2,3\} \] and \[ B=\{3,4\}. \] Find \[ A\times B \] and show it graphically. Solution The Cartesian product \(A\times B\) is the set

If A = {1, 2} and B = {1, 3}, Find A×B and B×A If \(A=\{1,2\}\) and \(B=\{1,3\}\), Find \(A\times B\) and \(B\times A\) Question If \[ A=\{1,2\} \] and \[ B=\{1,3\}, \] find \[ A\times B \] and \[ B\times A. \] Solution The Cartesian product \(A\times B\) is the set of all ordered

If a ∈ {2, 4, 6, 9} and b ∈ {4, 6, 18, 27}, Form Ordered Pairs (a, b) Such That a Divides b and a < b If \(a \in \{2,4,6,9\}\) and \(b \in \{4,6,18,27\}\), Form the Set of Ordered Pairs \((a,b)\) Such That \(a\) Divides \(b\) and \(a<b\) Question If \[ a \in

If a ∈ {-1, 2, 3, 4, 5} and b ∈ {0, 3, 6}, Write Ordered Pairs (a, b) Such That a + b = 5 If \(a \in \{-1,2,3,4,5\}\) and \(b \in \{0,3,6\}\), Write the Set of All Ordered Pairs \((a,b)\) Such That \(a+b=5\) Question If \[ a \in \{-1,2,3,4,5\} \] and \[ b