Educational

If A = {1, 2, 3}, B = {4}, C = {5}, Verify That A×(B∩C) = (A×B)∩(A×C) If \(A=\{1,2,3\}\), \(B=\{4\}\), \(C=\{5\}\), Verify That \(A\times(B\cap C)=(A\times B)\cap(A\times C)\) Question If \[ A=\{1,2,3\},\quad B=\{4\},\quad C=\{5\}, \] verify that \[ A\times(B\cap C)=(A\times B)\cap(A\times C). \] Solution \[ B\cap C=\phi \] \[ A\times(B\cap C)=A\times\phi=\phi \] \[ A\times B= \{ […]

If A = {1, 2, 3}, B = {4}, C = {5}, Verify That A×(B∪C) = (A×B)∪(A×C) If \(A=\{1,2,3\}\), \(B=\{4\}\), \(C=\{5\}\), Verify That \(A\times(B\cup C)=(A\times B)\cup(A\times C)\) Question If \[ A=\{1,2,3\},\quad B=\{4\},\quad C=\{5\}, \] verify that \[ A\times(B\cup C)=(A\times B)\cup(A\times C). \] Solution \[ B\cup C=\{4,5\} \] \[ A\times(B\cup C)= \{ (1,4),(1,5), \] \[ (2,4),(2,5),

If A = {2, 3}, B = {4, 5}, C = {5, 6}, Find A×(B∪C), A×(B∩C) and (A×B)∪(A×C) If \(A=\{2,3\}\), \(B=\{4,5\}\), \(C=\{5,6\}\), Find \(A\times(B\cup C)\), \(A\times(B\cap C)\) and \((A\times B)\cup(A\times C)\) Question If \[ A=\{2,3\},\quad B=\{4,5\},\quad C=\{5,6\}, \] find: \[ A\times(B\cup C), \] \[ A\times(B\cap C), \] and \[ (A\times B)\cup(A\times C). \] Solution \[

If A = {1, 2, 4} and B = {1, 2, 3}, Represent B×B Graphically If \(B=\{1,2,3\}\), Represent \(B\times B\) Graphically Question If \[ A=\{1,2,4\} \] and \[ B=\{1,2,3\}, \] represent the set \[ B\times B \] graphically. Solution The Cartesian product \(B\times B\) is the set of all ordered pairs \((b_1,b_2)\) where \[ b_1\in

Given A = {1, 2, 3}, B = {3, 4}, C = {4, 5, 6}, Find (A×B) ∩ (B×C) Given \(A=\{1,2,3\}\), \(B=\{3,4\}\), \(C=\{4,5,6\}\), Find \((A\times B)\cap(B\times C)\) Question Given \[ A=\{1,2,3\}, \] \[ B=\{3,4\}, \] and \[ C=\{4,5,6\}, \] find \[ (A\times B)\cap(B\times C). \] Solution \[ A\times B= \{ (1,3),(1,4), (2,3),(2,4), (3,3),(3,4) \} \]

If A = {1, 2, 4}, Represent A×A Graphically If \(A=\{1,2,4\}\), Represent \(A\times A\) Graphically Question If \[ A=\{1,2,4\}, \] represent the set \[ A\times A \] graphically. Solution The Cartesian product \(A\times A\) is the set of all ordered pairs \((a,b)\) where \[ a\in A \] and \[ b\in A. \] Given: \[ A=\{1,2,4\}

If A = {1, 2, 4} and B = {1, 2, 3}, Represent B×A Graphically If \(A=\{1,2,4\}\) and \(B=\{1,2,3\}\), Represent \(B\times A\) Graphically Question If \[ A=\{1,2,4\} \] and \[ B=\{1,2,3\}, \] represent the set \[ B\times A \] graphically. Solution The Cartesian product \(B\times A\) is the set of all ordered pairs \((b,a)\) where

If A = {1, 2, 4} and B = {1, 2, 3}, Represent A×B Graphically If \(A=\{1,2,4\}\) and \(B=\{1,2,3\}\), Represent \(A\times B\) Graphically Question If \[ A=\{1,2,4\} \] and \[ B=\{1,2,3\}, \] represent the set \[ A\times B \] graphically. Solution The Cartesian product \(A\times B\) is the set of all ordered pairs \((a,b)\) where

If A = {1, 2}, Find A×A and Then Form A×A×A If \(A=\{1,2\}\), Find \(A\times A\) and Then Form \(A\times A\times A\) Question If \[ A=\{1,2\}, \] first find \[ A\times A \] and then form \[ A\times A\times A. \] Solution Given: \[ A=\{1,2\} \] Step 1 : Find \(A\times A\) The Cartesian product

If A = {1, 2} and B = {3, 4}, Is A×(B ∩ Φ) = Φ True or False? State Whether the Statement is True or False: If \(A=\{1,2\}\), \(B=\{3,4\}\), Then \(A\times(B\cap\Phi)=\Phi\) Question State whether the following statement is true or false. If the statement is false, rewrite the statement correctly: If \[ A=\{1,2\},\quad B=\{3,4\},