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Example 31 Show That P Ab P A P B Chapter 1 Sets

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Ø ç ² X ¸ 8 á û × ¹ × L I î ø ü W D Q Þ q 1 & @ 8 Ë b Þ È 1 Þ q à 1 & a Ô ý W > ¤ 8 À Ò v Þ q Ý x À v > a v d > 8 ® S á j 8 Þ S î Ï v ² à ( 0EPS UISFTIPME v ² à ( Æ £ Ð x K È À D ç Ý º D v 3 P 8 û S × > b n 7 ª ( ýTo ask Unlimited Maths doubts download Doubtnut from https//googl/9WZjCW If `(bca)/a, (cab)/b,(abc)/c` are in AP, show that `1/a,1/b,1/c` are inIf Q(c) is true (case 2), then 9xQ(x) is true In either case, 9xP(x) _9xQ(x) is true Proof that 9x(P(x) _Q(x)) (= 9xP(x) _9xQ(x) Suppose 9xP(x) _9xQ(x) Breaking up by cases, if 9xP(x) is true (case 1), then P(c) is true for some c, and thus P(c) _Q(c) is true for that c If 9xQ(x) is true (case 2), then Q(d) is true for some d, and thus P(d

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