Find A x B, A x A and B x A (i) A = {2, -2, 3} and B = {1, -4} (i

1.	Find A x B, A x A and B x A (i) A = {2, -2, 3} and B = {1, -4} (ii) A = B = {p, q} (iii) A – {m, n} ; B = Φ
Answer» (i) A = {2, -2, 3} and B = {1, -4} A x B = {2,-2, 3} x {1,-4} = {(2, 1), (2, -4)(-2, 1) (-2, -4) (3, 1) (3,-4)} A x A = {2,-2, 3} x {2,-2, 3} = {(2, 2)(2, -2)(2, 3)(-2, 2) (-2, -2)(-2, 2) (3,-2) (3,3)} B x A = {1,-4} x {2,-2, 3} = {(1, 2)(1, -2)( 1, 3)(-4, 2) (-4,-2)(-4, 3)} (ii) A = B = {p, q} A x B = {p, q) x {p, q} = {(p,p),(p,q)(q,p)(q,q)} A x A = {(p,q) x (p,q)} = {(p,p)(p,q)(q,p)(q,q)} B x A = {p,q} x {p,q} = {(p,p)(p,q)(q,p)(q,q)} (iii) A = {m, n} x B = Φ Note: B = Φ or {} A x B = {m, n} x { } = { } A x A = {(m, n) x (m, n)} = {(m, m)(w, w)(n, m)(n, n)} B x A = { } x {w, n} = { }

Find A x B, A x A and B x A (i) A = {2, -2, 3} and B = {1, -4} (ii) A = B = {p, q} (iii) A – {m, n} ; B = Φ

Answer»

(i) A = {2, -2, 3} and B = {1, -4}

A x B = {2,-2, 3} x {1,-4}

= {(2, 1), (2, -4)(-2, 1) (-2, -4) (3, 1) (3,-4)}

A x A = {2,-2, 3} x {2,-2, 3}

= {(2, 2)(2, -2)(2, 3)(-2, 2) (-2, -2)(-2, 2) (3,-2) (3,3)}

B x A = {1,-4} x {2,-2, 3}

= {(1, 2)(1, -2)( 1, 3)(-4, 2) (-4,-2)(-4, 3)}

(ii) A = B = {p, q}

A x B = {p, q) x {p, q}

= {(p,p),(p,q)(q,p)(q,q)}

A x A = {(p,q) x (p,q)}

= {(p,p)(p,q)(q,p)(q,q)}

B x A = {p,q} x {p,q}

= {(p,p)(p,q)(q,p)(q,q)}

(iii) A = {m, n} x B = Φ

Note: B = Φ or {}

A x B = {m, n} x { }

= { }

A x A = {(m, n) x (m, n)} = {(m, m)(w, w)(n, m)(n, n)}

B x A = { } x {w, n}

= { }