\n 1\n <\/p>\n
\n 2. Suppose R and S are two equivalence relations on a set A. Prove that R \u2229 S is also an equivalence relation. (For an example of this, look at Figure 11.3. Observe that for the equivalence relations R2,R3 and R4, we have R2 \u2229 R3 = R4.)\n <\/p>\n
\n 3. Is the function \u03b8 : P(Z) \u2192 P(Z) defined as \u03b8(X) = X bijective? If so, find \u03b8 \u22121 .\n <\/p>\n
\n 4. Given f : A \u2192 B and subsets Y,Z \u2286 B, prove f \u22121 (Y \u2229 Z) = f \u22121 (Y)\u2229 f \u22121 (Z)\n <\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"
1 Show, if\u00a0n\u2208N\u00a0is not prime, then there exists\u00a0[a],[b]\u2208Z\u00a0such that\u00a0[a]\u2260[0]\u2260[b], but\u00a0[a]\u22c5[b]=[0]. Show, if\u00a0p\u2208N\u00a0is prime,\u00a0[a],[b]\u2208Z\u00a0and\u00a0[a]\u2260[0]\u2260[b], then\u00a0[a]\u22c5[b]\u2260[0]. 2. Suppose R and S are two equivalence relations on a set A. Prove that R \u2229 S is also an equivalence relation. (For an example of this, look at Figure 11.3. Observe that for the equivalence relations R2,R3 and R4, […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":"","_joinchat":[]},"categories":[1],"tags":[],"_links":{"self":[{"href":"https:\/\/qualityassignments.net\/wp-json\/wp\/v2\/posts\/227446"}],"collection":[{"href":"https:\/\/qualityassignments.net\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/qualityassignments.net\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/qualityassignments.net\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/qualityassignments.net\/wp-json\/wp\/v2\/comments?post=227446"}],"version-history":[{"count":0,"href":"https:\/\/qualityassignments.net\/wp-json\/wp\/v2\/posts\/227446\/revisions"}],"wp:attachment":[{"href":"https:\/\/qualityassignments.net\/wp-json\/wp\/v2\/media?parent=227446"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/qualityassignments.net\/wp-json\/wp\/v2\/categories?post=227446"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/qualityassignments.net\/wp-json\/wp\/v2\/tags?post=227446"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}