TRUE / FALSE 1. The intersection of two infinite sets is also infinite. 2. If A * B then ANB = Ø. 3. If two sets are disjoint, then their corresponding power sets are also disjoint.

Q: Only one of the following 5 statement is correct, choose the correct one Select one: O A. |A - B =…

A: Option (C) is correct.

Q: - For all sets A, B and C. Is (An B) U C =An (Bu C)? Justify your statement. You may ju

A: Yes, the above statement is false and the proof of above statement is given below:

Q: 5. Consider the sets A = 0 and B = {0} and C= {1,0}. Find each of the following sets, if it is…

A: The given sets are                       A=ϕ and B=ϕ and C=1,ϕ. Here the set A is the empty set,…

Q: Suppose that |A| = |B| = |C| = 6 and |A ∩ B| = |A ∩ C| = |B ∩ C| = 2. Determine the smallest that |A…

A: Given, |A| = |B| = |C| = 6 and |A ∩ B| = |A ∩ C| = |B ∩ C| = 2

Q: If a < b, then [a,b] CR does not have con- tent 0. In fact, if U1,. . .,Un) is a finite cover of…

A:

Q: If A = {x: x |B| D. None of these {x: x 2 + 11x + 30 = 0,x E N}, then C is a/an? A. Empty set B.…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: 3. Define two sets, call them A and B, that makes the following statement true; if it is impossible…

A:

Q: 4. Prove or disprove For all sets A. B and C. if A OC-0,then A. B and Care your answers as ar AUD,…

A: The given statement is FALSE.

Q: Which of the following are difference sets? (iii) {3, 6, 7, 12, 14} in Z21.

A:

Q: Which of the following sets are equal? B = {d, e, a, c} A = {a, b, c, d} C = {d, b, a, c} D = {a, a,…

A: The given sets are A = {a, b, c, d}, B = {d, e, a, c} C = {d, b, a, c} and D = {a, a ,d, e, c, e}.It…

Q: The boundary of a set is equal to the boundary of the complement True O False O

A: A point of a set is called boundary points if any neighbourhood of this point contains point of the…

Q: can two disjoint sets be close? Justify your answer using an example.

A: We know that any closed interval of the form [a,b] is an closed set. We use this fact further.

Q: a) Disjoint, non-empty sets A, B, and C such that Aº N (BUC)= A° Is there such an example?

A: Soln :- Disjoint, non-empty sets A,B &amp; C such that  ACn (B∪C)=Ac Yes,      One can always find…

Q: If either A or B empty set then Ax B equal empty O A

A: The solution is given as

Q: If ? = {₤,₱,$, ¥} and ? = {♥, ♠, ♦, ♣}, which of the following statement(s) is/are NOT true? i. The…

A: If there are two sets - set Aand set B Equivalent sets are sets if there are same number of elements…

Q: Describe the set ?={?:|?^2−5|&gt;6} as a union of finite or infinite intervals.

A: The given set is A = {x: |x2–5|&gt;6}. Apply the absolute rule on the condition as follows.

Q: Which of the following are disjoint sets?* O D. (1,3,5) and (2,4,6) B. (1,2,3) and (2,3,4) O c.…

A:

Q: Another operation that can be defined on sets A and B is the difference of the sets, denoted by A -…

A: The given universal set is                                       U={1,2,3,4,5,6,7,8,9}    and the…

Q: Which of the following are disjoint sets? O B.(1,2,8) and (2,8,4) O C (1,2,5) and (3,4,5) (1,8,5)…

A: Given the sets:  1,2,3 and 2,3,4 1,2,5 and 3,4,5 1,3,5 and 1,3,6 1,3,5 and 2,4,6 We have to check…

Q: If A and B are sets; Aºand Bºdenote the complements of the sets A and B, then the set (A – B) U (B –…

A: Given:- If A and B are sets; Ac and Bc denote the complements of the sets A and B, then the set (A -…

Q: Which of these are sets having the 2nd element as the inverse of the 1st element? A. (D,A) and…

A: Use the definition of identity and inverse element.

Q: Give me Example of the ff. sets 1. Equivalent Sets 2. Disjoint Sets 3. Empty sets 4.…

A: In this question we just want to write  the examples of different sets

Q: 4.1 Write down the identity element of the set and substantiate. 4.2 Write down the set of inverse…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for you…

Q: simplify each of the following sets and state whether the set is finite, countably infinite or…

A:

Q: Which of the following are disjoint sets?* B.(1,2,3) and (2,3,4) O (1,2,5) and (3,4,5) O (1,3,5) and…

A: Topic:- set theory If the two sets A and B are disjoint then they have no elements in common that is…

Q: (10) Show that the set A = {a € Q : a² < 2 or a < 0} is a %3D cut.

A:

Q: R, S and T are closed sets implies RnSnT is closed.

A: given

Q: If X = {£, P, $) and Y = {0,0,0), which of the following statement(s) is/are NOT true? i. The two…

A: The objects of the sets X and Y are totally different that is they have no common element as such.…

Q: Which of the following sets is closed in (R, Tu)? O a. { ne N}U{2} 72 2n O b. Q-N c. O c. [2,5) U…

A: Determine the meaning of ℝ, τu. Now, go with each option and check which is correct.

Q: Which of the following sets are equal? A = { 0, 1, 2 } B = { x ∈ R | -1 ≤ x < 3 } C = { x ∈ R | -1 <…

A:

Q: How may sets of intersecting chords are there in the figure? [6 1 12 14 73° 4 1

A: Q.6 has answer 3

Q: a) DeMorgan's laws tell us that for sets A and B, the expression (Aº n Bº)° simplifies to

A: For two sets A and B the De Morgan's Law states that A∩BC=AC∪BC.

Q: 사 Use the Venn diagram shown to the right to determine whether the given sets are equal for all sets…

A: Given below clear explanation

Q: Answer the questions with Yes or No, and then explain why yes or why not. Justify your answer. Does…

A: The equality A∪B=A+B is not always true for every sets A and B. It is true only when A and B are…

Q: (a) By contradiction, prove that V r, y € Z, if ry is even and y is odd then x is even. (b) Show…

A: (a) Given v x,y ∈Z,     &amp; xy is an even integer with y is odd.     To show x is even.      Let…

Q: Which of the following statements is true OA For all sets A, B and C. if AUC=BUC then A =B. O B. For…

A:

Q: 3. Let A = (4,5,6) and B (5,6,7}, (x, y) ER means that is an integer, write the %3D ordered pair of…

A: A={4,5,6} and B={5,6,7}, (x,y)∈R means that x+y2 is an integer

Q: 3.* Show that (A \ B) \ C = A \ (BUC). Is (A \ B)\C = A\ (B\C)? 4.* If A and B are sets, we define…

A: Set equality proof

Q: Is this set finite or infinite? {x € R|1 < x < 2}

A:

Q: If A and B are two sets satisfying A∖B=B∖A what can we conclude about A and B? Explain.

A:

Q: 28. Which of the following sets does not have the completeness axiom? A. R {0} B. R+ C. Q {0} D. R…

A: We have to determine which sets doesn't have the completeness axiom .

Q: Two sets are said to be disjoint if their intersection is zero. Select one: O True O False

A:

Q: our answer Prove or disprove For all sets A. B and C, ir ABOC-0, then A. B and C are UD. AN, A.A-B.…

A:

Q: The symmetric difference of two sets A O B is the set of elements that are in either the set A, or…

A: The aim is to show that, A⊕(B⊕C)=(A⊕B)⊕C It is known that, A⊕B=A∪B-A∩B So A⊕(B⊕C) can be written as,…

Q: Show that the set EE is: (ii). Closed iff E¯=E

A: Show that the set E is Closed iff E¯=E

Q: Prove by contradiction that for any sets A and B , if A∩(B∪C)= ∅ and B⊆C, then B-(A∪C)=∅.

A:

Q: Let A and B be sets. Then B - (B - A) ANB is equal to the above Ā NB is equal to the above

A: Here ,we are given that A and B are two sets. We need to find  B-(B-A) : Now, Here ( B-A) represents…

Q: 2.3 Show that the following sets don't satisfy the law of contradiction and the law of excluded…

A: part(a) GIVEN μAx=11+x TO SHOW: given function don't satisfy the following laws 1) law of…

Q: Which of the following sets is (are) closed under multiplication? Explain why or why not. d.{0, 1}…

A: (d) the set {0,1} is closed under multiplication, because, 0•0 = 0, 0•1 = 0, 1•0 = 0 &amp;, 1•1 = 1