1.1 Show that the following sets satisfy the law of contradiction and law ofexcluded middle.X = {a, b, c, d, e, f, g}A = {a, b, c, d}

Consider the following sets. The universal set U for this problem is the set of all residents of India. A = the set of all English speakers B = the set of all Hindi speakers C = the set of all Urdu speakers Express the following sets in the symbols of set theory. (a) Residents of India who speak English, Hindi, and Urdu. O (ANBNC)' OAN (BUC) O (AU BUC)' ОАПВПС O AU BUC (b) Residents of India who do not speak English, Hindi, or Urdu. ОАПВПС O (AU BUC)' OAN (BUC) O AUBUC O (ANBNC)' (c) Residents of India who speak English, but not Hindi or Urdu. O (ANBNC)' О АП ВПС OAN (BUC) O (AU BUC)' O AUBUC

a. Is 3 ∈ {1, 2, 3}? b. Is 1 ⊆ {1}? c. Is {2} ∈ {1, 2}?

9. Is the following statement TRUE or FALSE? If it is TRUE, prove it, and if it is FALSE, provide a counter-example.If f: S→T is a function, where |S| > |T| (and both are finite sets), then there exist elements s1 and s2 in S such that fs1()=fs2()

please show the correct answer and steps (10)

Prove: If a set A is a subset of the empty set, then A itself has to be an empty set.

Let A = {1, 2, 3},         B = {{1}, 2, {1, 3}},         C = {1, {1}, 3}.   Compute the following sets:                                                                         2A∩C − B,         (A ∩ B) × (A − C),         (B ∪ C) − A.

Please explain the answers and show the solouton! F1

Given set A = {1,2,{3},4,5,{1,2},7}, the possible subsets of set A are {1,2,3,4,5,1,2,7} {1, 2, {3}} {1,2,1,2,1,2,1,2}

a) State the inverse and contrapositive of the statement "W whenever he comes". b) Let A, B and C be sets. Prove that A-(A-B) = A N B. c) Find all m 2 1 such that 27 = 9 (mod m). %3D