Math, asked by maheshnayak2424, 11 months ago

If
A= (x:x is odd number and x < 10) and
B={x:x is prime number and x<10), then show that A-B#B-A.​

Answers

Answered by MaheswariS
0

\underline{\textbf{Given:}}

\mathsf{A=\{x:\;x\;is\;a\;odd\;number\;and\;x\;&lt;\;10\}}

\mathsf{B=\{x:\;x\;is\;a\;prime\;number\;and\;x\;&lt;\;10\}}

\underline{\textbf{To show:}}

\mathsf{A-B\,{\neq}\,B-A}

\underline{\textbf{Solution:}}

\underline{\textbf{Difference of two sets:}}

\textsf{Let A and B be two sets. Then,}

\boxed{\mathsf{A-B=\{x:\;\;x\,\in\,A\;and\;x\,\notin\,B\}}}

\mathsf{Clealry,}

\mathsf{A=\{1,3,5,7,9\}}

\mathsf{B=\{2,3,5,7\}}

\mathsf{A-B=\{1,3,5,7,9\}-\{2,3,5,7\}}

\implies\boxed{\mathsf{A-B=\{1,9\}}}--------(1)

\mathsf{B-A=\{2,3,5,7\}-\{1,3,5,7,9\}}

\implies\boxed{\mathsf{B-A=\{2\}}}--------(2)

\textsf{From (1) and (2), we get}

\mathsf{A-B\,{\neq}\,B-A}

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