If A,B and C are sets, then A x (B-C) = (A × B)- (A x C). |

Q: Write true otherwise false if the pairs of sets are equal,{{1}},{1,{1}}

A: Two sets A and B are equal if A and B  have the same elements.

Q: If set A X B=B X A then which of the following sets may satisfy

A: CARTESIAN PRODUCT The cartesian product of set X to the set Y is given by the set of all possible…

Q: For any sets A and B , (ANB) = %3D O a. ANB O b. ANB Oc. B-A С. В- А O d. U-B

A: By using identities of set theory :

Q: If P = {a, b, c} and Q = {r}, form the sets P × Q and Q × P. Are these two products equal?

A: P × Q = {a,b,c} × {r} = {(a,r) , (b,r) , (c,r) } Q × P= {r} × {a,b,c} = { (r,a) , (r,b) , (r,c) }

Q: (b) Show that the set A = {(x, y) E R² : y > 0} is not complete.

A: Given: The given set ,

Q: Come up with an open interval A and closed interval B such that A∪B = (0, 4) and A ∩ B = [1, 2].

A:

Q: Give an example of sets A and B for which |A U B| = |A|+|B|.

A:

Q: Let S = (x: (x - 1)² = 0}, state where S is singleton set or not.

A:

Q: Suppose A and B are sets such that |A| = 2 and |B| = 3. What is |P(A x B)|?

A:

Q: Ex 3.7.1 Construct the correspondences between the indicated sets. a) Z10 and Z2 × Zg b) Z15 and Z3…

A:

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: d) Suppose X = {1,2, 3} and Y = {5,6}. The number of elements of the set P(X× Y) =

A: Elements in X = 3. Elements in Y = 2 Elements in X × Y = 3 × 2 = 6

Q: Đ A is a closed set.

A:

Q: & and X are open sets.

A:

Q: Which of the following set is empty a. {x: x = x} b. { x : x != x 2 } c. { x : x ! = x } d. {x:…

A: Empty set:            The empty set is the unique set having no elements. and its cardinality is…

Q: Let A and B be two sets. We denote A- B = { x | x∊A and xÏB}. Prove that A∪B=(A−B)∪(A∩B)∪(B−A).

A:

Q: If A = {(x, y): (2, -2), (4, -1), (6, 0), . . .}, complete the rule for set A. y= 1/2x - 3 -1/2x -…

A: Observe the given pattern of set A then complete the rule.

Q: if A and B are sets, then A x B=B x A

A:

Q: Let A and B be sets.                                   If A ∩ X = B ∩ X = φ and A ∪ X = B ∪ X for…

A:

Q: Let A, B, C, D be sets. (ANB)x(CND)=(AXC)n(BxD). True. False.

A: Use the basic properties of intersection and cartesian product to prove the given relation.

Q: The closure for set P would be the set |z-(1+i)| = 2 |z(1+i)= 3 |z- (1 + i)| < 1 None of the above…

A:

Q: Give an example of three sets A,B and C such that A ⊆ B, B ⊆ C, C 6⊆ A and C ⊆ B.

A: We construct  an example of three sets A,B and C such that A ⊆ B, B ⊆ C, C 6⊆ A and C ⊆ B.

Q: Find an example of sets A and B such that |A|=3,|A|=3, |B|=4,|B|=4, and |A∪B|=5.

A: Let A = {2, 3, 4} and |A|= 3 and B = {2, 4, 6, 8} and |B|= 4 The union of set A and B is the set of…

Q: ( Prove that the set {a E R2: a2 ... Prove that the set {a E R2: a2 not equal to 6} is open.

A: Let the set is A=a1,a2∈ℝ2:a2≠6 The objective is to prove that the set A is open.

Q: Let A and B be sets then A + B if, and only if A ¢ B or B ¢ A. 8. For sets A, B, and C, A U (B N C)…

A: True or False :  (7)  Let A and B be sets , then  A≠B if and only if  A ⊄ B or B ⊄A. (8) For sets A,…

Q: Assume that the statement applies to all sets. Is it true or false? A – (BO C) = (A – B) (A – C) 2.

A: A-(B INTERSECTION) C= (A-B)INTERSECTION(A-C)

Q: Which of the following is true for any set A?

A: HERE FOR TRUE SENTENCE FOR ANY SET A . EMPTY SET IS  SUBSET OF ANY SET

Q: If A, B, C are sets, show that a) A x B= 0 ⇒ A=0 or B = 0. b) (AUB) x C = (AXC) U (BxX C). c) (An B)…

A:

Q: ) Suppose X = {1,2, 3} and Y = {5,6). The number of elements of the set P(X × Y) = %3D

A: Number of Elements in Power Set P(A) of set A with n elements is 2n

Q: For sets A, B and C, prove that (A∩B) x C = (A x C)∩(B x C).

A: For sets A, B and C, prove that (A∩B) x C = (A x C)∩(B x C).

Q: Let A = {a,b,c,d} be the set containing the four elements a, b, c and d. Let S = {X |X is a subset…

A: Sets

Q: Suppose A={-1, 0, 4}.Find a set B such that A is equivalent to B.

A: Two sets A and B are said to be equivalent to each other if both the sets A and B have same number…

Q: If X and Y are two sets such that           n ( X ) = 17, n ( Y ) = 23 and                    n ( X…

A:

Q: 12. Find two sets A and B such that A e B and A B.

A: 12.Find two sets A and B such that A∈B and A⊑B

Q: If A and B are any two sets and A U B = A ∩ B, then a. A= Ø b. B= Ø c. A=B d. None of these

A: topic - sets option C.   A=B

Q: If A and B are sets such that ACB then A × BC B x B. true false

A:

Q: if A and B are set, then A x B=B x A  True or False

A:

Q: For all sets A and B, ifA-B=0, then A = B.

A: For all sets A and B, if A-B=∅, then A=B.

Q: 4. Write the set in the form (x P(x)}, where P(x) is a property that describes the elements of the…

A:

Q: If X = {u,v} what is the power set of X? (in answering this question, use {} as the null set, and do…

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Q: Let A, B and C be non-empty sets and let X= (A-B)-C and Y=(A-C)-(B-C) .Check whether X=Y or not.

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Q: Decide whether the statement is true or false. Two set A and B are equal if have the same number of…

A:

Q: TRUE (c) The union of two sets, A and B, is the set of all elements in A and B. FALSE

A: We have to say whether it is true or not " The union of two sets A and B is the set of all elements…

Q: Define the sets A, B, C, and D as follows: A = {-3, 0, 1, 4, 17} B = {-12, -5, 1, 4, 6} C= {x € Z: x…

A: Intersection collect all common elements and in union collect all elements

Q: Express (4, 10) as a set {x: Ix - al&lt; c} for suitable a and c.

A:

Q: If X and Y are two sets, then X∩(Y∩X)c equals a. Ø b. Y c. X d. X∩Yc

A:

Q: Let A and B be two sets such that n(A) = 3 and n(B) = 2. If (x, 1), (y, 2), (z, 1)are in A × B, find…

A: In AxB the first element will be from A and the second element will be from B So, x,y,z are in A And…

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…