 # 7 show that if A is 9 collection of induct tive sets, then the int...

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7 show that if A is 9 collection of induct tive sets, then the intersection of the elements of A is an inductive set? b poove the basic properties (1) and(2) oft, 8 a prove by induction that given nez, every nonemptr subset + of E1,-in? has alargest element? b Explain why You can not conclude from(a) that exer r inonemptr sebset of Z, has alargest element? 9 prove that the function f defined bijective? f(x)= ger ) iff iff X*9 nt/ x=90 orderpreserving bijection fiA-E63 - 6 Sir f(x) = f(x) iff XE A-E6} n+1 iff xeb . show that of is in fact order preserving? C poove that Leb A be afinite set and suppose that BCA IFB is a aproper subset of A then the cardinality of (Bis strictlyless than the cardinality of A?decead / show there is abjective correspondence of AXB with BXA? 2 show that if B is not finite and BCA, then A is not finite? 3 If AXB is finite, does it follow that A and 13 are finite ? 4 a Let A=E1, win? show there is abijection of p(A)With the cartesian product **, where xis the two, element set X=40,13? 6 show that if A is finite, then p(A)is finite? 5 poove that following "laws of algebra 11:- 6 prove the following "laws of inequalities a If Xty =X, then Y=0 9 X>Yandwyze X+W >ytz 6 O.X=0 [Hint. Computer(xto). X 6 X>oand. you xty7oand x.y70 C - O=O C OXYOES-KKO I -(X) =X d OXSYED-KC-Y. CO e x>yandzco x7D1-11*==X DX#O 1270, where x==.X )-KOCZ. h h i Y=1 or bothnegative. th positive j XIX=1 ifx*0 Dx>o 21x70. U 1x4940 K XII=X 1/X< 1/Y I X#O and you ) KXYFO m 11 (XIY) P X#0 11x 9 2/1w1Z) =zwifwitzo t 770. s = t Y #0.

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