%3Cp%3E%3Cspan%20style%3D%22color%3A%26nbsp%3Brgb(34%2C%26nbsp%3B34%2C%26nbsp%3B
ID: 2846061 • Letter: #
Question
%3Cp%3E%3Cspan%20style%3D%22color%3A%26nbsp%3Brgb(34%2C%26nbsp%3B34%2C%26nbsp%3B34)%3B%26nbsp%3Bfont-family%3A%26nbsp%3Barial%2C%26nbsp%3Bsans-serif%3B%26nbsp%3Bfont-size%3A%26nbsp%3B13.333333969116211px%3B%22%26nbsp%3Bdata-mce-style%3D%22color%3A%26nbsp%3B%23222222%3B%26nbsp%3Bfont-family%3A%26nbsp%3Barial%2C%26nbsp%3Bsans-serif%3B%26nbsp%3Bfont-size%3A%26nbsp%3B13.333333969116211px%3B%22%3EPlease%26nbsp%3Bprove%26nbsp%3Bthe%26nbsp%3Bfollowing%26nbsp%3Bproof%26nbsp%3Bwithout%26nbsp%3Bpictures%2C%26nbsp%3Band%26nbsp%3Bprofessionally%26nbsp%3Bwritten.%26nbsp%3BYou%26nbsp%3Bmay%26nbsp%3Bofcourse%26nbsp%3Buse%26nbsp%3BSet%26nbsp%3BLogic%26nbsp%3Bsymbols.%26nbsp%3B%3C%2Fspan%3E%3C%2Fp%3E%3Cp%3E%3Cspan%26nbsp%3Bstyle%3D%22font-size%3A%26nbsp%3Blarge%3B%22%3E%3Cstrong%3E%3Cspan%26nbsp%3Bcolor%3D%22%23222222%22%26nbsp%3Bface%3D%22arial%2C%26nbsp%3Bsans-serif%22%26nbsp%3Bsize%3D%222%22%26nbsp%3Bstyle%3D%22color%3A%26nbsp%3Brgb(34%2C%26nbsp%3B34%2C%26nbsp%3B34)%3B%26nbsp%3Bfont-family%3A%26nbsp%3Barial%2C%26nbsp%3Bsans-serif%3B%22%26nbsp%3Bdata-mce-style%3D%22color%3A%26nbsp%3B%23222222%3B%26nbsp%3Bfont-family%3A%26nbsp%3Barial%2C%26nbsp%3Bsans-serif%3B%22%3E%3Cbr%3E%3C%2Fspan%3E%3C%2Fstrong%3E%3C%2Fspan%3E%3C%2Fp%3E%3Cp%3E%3Cspan%26nbsp%3Bstyle%3D%22font-size%3A%26nbsp%3Bxx-large%3B%22%3E%3Cstrong%3E%3Cspan%26nbsp%3Bcolor%3D%22%23222222%22%26nbsp%3Bface%3D%22arial%2C%26nbsp%3Bsans-serif%22%26nbsp%3Bsize%3D%222%22%26nbsp%3Bstyle%3D%22color%3A%26nbsp%3Brgb(34%2C%26nbsp%3B34%2C%26nbsp%3B34)%3B%26nbsp%3Bfont-family%3A%26nbsp%3Barial%2C%26nbsp%3Bsans-serif%3B%22%26nbsp%3Bdata-mce-style%3D%22color%3A%26nbsp%3B%23222222%3B%26nbsp%3Bfont-family%3A%26nbsp%3Barial%2C%26nbsp%3Bsans-serif%3B%22%3EProve%3A%26nbsp%3BIf%26nbsp%3BA%26nbsp%3Band%26nbsp%3BB%26nbsp%3Bare%26nbsp%3Bsets%26nbsp%3Bthen%26nbsp%3BA%26nbsp%3Bis%26nbsp%3Ba%26nbsp%3Bsubset%26nbsp%3Bof%12%26nbsp%3BB%26nbsp%3Bif%26nbsp%3Band%26nbsp%3Bonly%26nbsp%3Bif%26nbsp%3BB'%26nbsp%3Bis%26nbsp%3Ba%26nbsp%3Bsubset%26nbsp%3Bof%26nbsp%3B%12A%3C%2Fspan%3E%3C%2Fstrong%3E%3C%2Fspan%3E%3C%2Fp%3E%3Cp%3E%3Cspan%26nbsp%3Bstyle%3D%22color%3A%26nbsp%3Brgb(34%2C%26nbsp%3B34%2C%26nbsp%3B34)%3B%26nbsp%3Bfont-family%3A%26nbsp%3Barial%2C%26nbsp%3Bsans-serif%3B%26nbsp%3Bfont-size%3A%26nbsp%3B13.333333969116211px%3B%22%26nbsp%3Bdata-mce-style%3D%22color%3A%26nbsp%3B%23222222%3B%26nbsp%3Bfont-family%3A%26nbsp%3Barial%2C%26nbsp%3Bsans-serif%3B%26nbsp%3Bfont-size%3A%26nbsp%3B13.333333969116211px%3B%22%3E%3Cbr%3E%3C%2Fspan%3E%3C%2Fp%3E%3Cp%3E%3Cspan%26nbsp%3Bstyle%3D%22color%3A%26nbsp%3Brgb(34%2C%26nbsp%3B34%2C%26nbsp%3B34)%3B%26nbsp%3Bfont-family%3A%26nbsp%3Barial%2C%26nbsp%3Bsans-serif%3B%26nbsp%3Bfont-size%3A%26nbsp%3B13.333333969116211px%3B%22%26nbsp%3Bdata-mce-style%3D%22color%3A%26nbsp%3B%23222222%3B%26nbsp%3Bfont-family%3A%26nbsp%3Barial%2C%26nbsp%3Bsans-serif%3B%26nbsp%3Bfont-size%3A%26nbsp%3B13.333333969116211px%3B%22%3ETIPS%3A%26nbsp%3BTHERE%26nbsp%3BIS%26nbsp%3BNO%26nbsp%3BTYPO.%26nbsp%3BConvince%26nbsp%3Byourself%26nbsp%3Bit's%26nbsp%3Btrue%26nbsp%3Bbefore%26nbsp%3Byou%26nbsp%3Btry%26nbsp%3Bto%26nbsp%3Bprove%26nbsp%3Bit.%26nbsp%3BPick%26nbsp%3Ba%26nbsp%3Brandom%26nbsp%3Bset%26nbsp%3Bfor%26nbsp%3Bthe%26nbsp%3Buniverse%26nbsp%3Bto%26nbsp%3Bbe%2C%26nbsp%3Bpick%26nbsp%3Ban%26nbsp%3BA%26nbsp%3Band%26nbsp%3BB%26nbsp%3Band%26nbsp%3Bsee%26nbsp%3Bif%26nbsp%3Bit's%26nbsp%3Btrue.%26nbsp%3BIf%26nbsp%3Bit's%26nbsp%3Bnot-%26nbsp%3Bthat%26nbsp%3Bshould%26nbsp%3Btell%26nbsp%3Byou%26nbsp%3Bsomething.%26nbsp%3BIf%26nbsp%3Bit%26nbsp%3Bus%2C%26nbsp%3Bhopefully%26nbsp%3Bthe%26nbsp%3Bmessing%26nbsp%3Baround%26nbsp%3Bwill%26nbsp%3Bprovide%26nbsp%3Binsight.%3C%2Fspan%3E%3Cbr%26nbsp%3Bstyle%3D%22color%3A%26nbsp%3Brgb(34%2C%26nbsp%3B34%2C%26nbsp%3B34)%3B%26nbsp%3Bfont-family%3A%26nbsp%3Barial%2C%26nbsp%3Bsans-serif%3B%26nbsp%3Bfont-size%3A%26nbsp%3B13.333333969116211px%3B%22%26nbsp%3Bdata-mce-style%3D%22color%3A%26nbsp%3B%23222222%3B%26nbsp%3Bfont-family%3A%26nbsp%3Barial%2C%26nbsp%3Bsans-serif%3B%26nbsp%3Bfont-size%3A%26nbsp%3B13.333333969116211px%3B%22%3E%3Cbr%26nbsp%3Bstyle%3D%22color%3A%26nbsp%3Brgb(34%2C%26nbsp%3B34%2C%26nbsp%3B34)%3B%26nbsp%3Bfont-family%3A%26nbsp%3Barial%2C%26nbsp%3Bsans-serif%3B%26nbsp%3Bfont-size%3A%26nbsp%3B13.333333969116211px%3B%22%26nbsp%3Bdata-mce-style%3D%22color%3A%26nbsp%3B%23222222%3B%26nbsp%3Bfont-family%3A%26nbsp%3Barial%2C%26nbsp%3Bsans-serif%3B%26nbsp%3Bfont-size%3A%26nbsp%3B13.333333969116211px%3B%22%3E%3Cbr%3E%3C%2Fp%3EExplanation / Answer
We want to show the following: If (A) and (B) are set, then (A subset B) if and only if (B' subset A').
Assume (A subset B). Let (x in A). Since (A subset B), (x in B). Then, (x otin B'). But since (x in A), then (x otin A'). Thus, (B' subset A').
Now, assume (B' subset A'). Let (x in B'). Then, (x in A') and (x otin A). But since (x in B'), then (x otin B'). Therefore, (A subset B).
Let me know if you have any comment.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.