tag:blogger.com,1999:blog-8342347821869463061.post4494195754666908345..comments2023-11-02T17:30:26.989+05:30Comments on My Technical Scratch Pad.: how to prove it - ch4, sec4.2(Relations)himanshuhttp://www.blogger.com/profile/02909790425038294533noreply@blogger.comBlogger12125tag:blogger.com,1999:blog-8342347821869463061.post-7656455167577128282021-01-29T05:17:57.581+05:302021-01-29T05:17:57.581+05:30For example 4, why is (2,5) not apart of aFor example 4, why is (2,5) not apart of a43-Mu-Gammahttps://www.blogger.com/profile/06799659049423896256noreply@blogger.comtag:blogger.com,1999:blog-8342347821869463061.post-60954666105890451382020-01-18T10:31:52.510+05:302020-01-18T10:31:52.510+05:30I think the proof of 11(a) is correct. The goal i...I think the proof of 11(a) is correct. The goal in this question requires you to show that $(a,c) \in (S \setminus T) \circ R$. All you need to do is show some b exist s.t. $(a,b) \in R$ and $(b,c) \in S$. 12(b) on the other hand requires showing $(a,c) \notin T \circ R$. This requires showing $\lnot \exists b \in B ( (a,b) \in R \land (b,c) \in T)$. fesodeshttps://www.blogger.com/profile/17761308025984234595noreply@blogger.comtag:blogger.com,1999:blog-8342347821869463061.post-49673570293803835962017-04-11T19:03:37.377+05:302017-04-11T19:03:37.377+05:30Can't we also prove Ex-10 by contrapositive in...Can't we also prove Ex-10 by contrapositive in both directions?Adamhttps://www.blogger.com/profile/14013653878402950925noreply@blogger.comtag:blogger.com,1999:blog-8342347821869463061.post-72367406262520486952015-10-31T04:54:45.565+05:302015-10-31T04:54:45.565+05:30Ex-6d: there is a typo in the last iff (c,a)∈(S-1∘...Ex-6d: there is a typo in the last iff (c,a)∈(S-1∘R-1), it should be: (c,a)∈(R-1∘S-1). Also in the last line.Jos van Weerthttps://www.blogger.com/profile/04247588707452816386noreply@blogger.comtag:blogger.com,1999:blog-8342347821869463061.post-16906445518611660502015-06-29T02:59:37.683+05:302015-06-29T02:59:37.683+05:30You proof of 11.a is incorrect for the same reason...You proof of 11.a is incorrect for the same reason that the proof in the book given in 11.b is incorrect. That is, the statement "Since (a,c)∉T∘R, so clearly (b,c)∉T" is wrong.Unknownhttps://www.blogger.com/profile/10211772733357210499noreply@blogger.comtag:blogger.com,1999:blog-8342347821869463061.post-88145625901678429252015-06-29T02:56:38.458+05:302015-06-29T02:56:38.458+05:30The problem is in the statement "since (a, b)...The problem is in the statement "since (a, b) ∈ R and (b, c) ∉ T, (a, c) ∉ T ∘ R". At that point in the proof b is a specific object, but to say that "(a, c) ∉ T ∘ R" means ¬∃b' ∈ B((a, b') ∈ R ∧ (b', c) ∈ T). Alternatively, ∀b'∈B((a, b') ∉ R ∨ (b', c) ∉ T). Since b was just a specific object, the latter assertion does not follow.Unknownhttps://www.blogger.com/profile/10211772733357210499noreply@blogger.comtag:blogger.com,1999:blog-8342347821869463061.post-39474412495009300132015-06-28T02:19:34.908+05:302015-06-28T02:19:34.908+05:30Agree with Stavros Mekesis. The domain of 2-b is {...Agree with Stavros Mekesis. The domain of 2-b is {x | x ≤ -1 ∨ x ≥ 1} and the range is {y | 0 < |y| < 1} = {y | -1 < y < 1}.Unknownhttps://www.blogger.com/profile/10211772733357210499noreply@blogger.comtag:blogger.com,1999:blog-8342347821869463061.post-61210849279764490242015-06-28T02:19:03.378+05:302015-06-28T02:19:03.378+05:30This comment has been removed by the author.Unknownhttps://www.blogger.com/profile/10211772733357210499noreply@blogger.comtag:blogger.com,1999:blog-8342347821869463061.post-18501967659859385072014-11-10T02:10:11.108+05:302014-11-10T02:10:11.108+05:30What its wrong with it then?What its wrong with it then?Hernitorrincohttps://www.blogger.com/profile/00466160621021875833noreply@blogger.comtag:blogger.com,1999:blog-8342347821869463061.post-84105147294069510772013-11-26T02:36:16.545+05:302013-11-26T02:36:16.545+05:30Ex - 5 b) one more pair is (4,3)Ex - 5 b) one more pair is (4,3)Palakhttps://www.blogger.com/profile/14932814865789230296noreply@blogger.comtag:blogger.com,1999:blog-8342347821869463061.post-9769626663148613362013-08-29T23:47:57.807+05:302013-08-29T23:47:57.807+05:30Ex-11
(b) The proof is not correct.
(c) Counterex...Ex-11<br />(b) The proof is not correct.<br /><br />(c) Counterexample: <br />S = {(3,2)}<br />T = {(1,2)}<br />R = {(1,3), (1,1)}<br /><br />Then<br />(S\T)oR = {(1,2)}<br />(SoR)\(ToR) = ∅Unknownhttps://www.blogger.com/profile/09516156841806325513noreply@blogger.comtag:blogger.com,1999:blog-8342347821869463061.post-89909840813820733112013-08-28T22:11:52.811+05:302013-08-28T22:11:52.811+05:30Ex-2
(b) I found the following: Domain = (-oo, -1]...Ex-2<br />(b) I found the following: Domain = (-oo, -1] U [1, +oo) and Range = (-1,1).<br />Unknownhttps://www.blogger.com/profile/09516156841806325513noreply@blogger.com