5. State whether each of the following statements is true or false, in either case substan- tiate/ justify. (g) The empty set is path-connected.

Q: 9. What is the set-builder equivalent of {0, 1, 2 }? 10. What is the set-roster equivalent of {x E…

A: Set: Set is any collection of objects or elements which may be numerical or non-numerical. Set…

Q: 13. Let X and Y be subsets of any finite, nonempty set. Give the properties of the relation where X…

A:

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: 3. Find an example of two nonempty sets A and B for which A x B = Bx A is true.

A: To find an example of two nonempty sets A and B for which AXB=BXA

Q: 37. Which of these three statements is/are not true? I: Every finite nonempty subset of R has a…

A: We shall answer all the parts and provide justification as to why a particular part is not true. In…

Q: Provide 2 examples of sets with |A| = 4, |B| = 3, |AUB| = 6

A: Number of elements in set A is 4, in set B is 3 and in set A U B is 6.

Q: 9. Show that the property of "having nonempty open sets with a finite number of points" is a…

A:

Q: If S is a relation from a non-empty set A to a nonempty set B then

A: Solution :-

Q: 3. Let R be the universal set and D = (-7,4], E = (0,8), F = {r: r ≤ 10, r € R} be the subsets of X.…

A:

Q: Assume that the universal set is Z. Consider the following sentence: (3t = Z) (t •x = 20). (a)…

A: Here, in the question, it says, such that tx= 20.We know a statement in logic and mathematics is a…

Q: Identify the type of set (finite, infinite or empty) as described by the following: 1. A = {stars in…

A: A set is said to be finite if it contains only finite number of elements. A set is said to be…

Q: Q.Prove If ANB is pathwise connected set, then A andB are or disprove the following: pathwise…

A:

Q: A and B be two sets, and A - B = . a) What can you say about sets A and B? b) Draw a Venn diagram.

A:

Q: Let A = {7m +1 : m € Z} and B = {14n – 6 : n € Z} be subsets of a universal set U. Justify why A ¢ B…

A: Consider the given sets:

Q: Can you explain what the process was to find the cardinality?

A: Cardinality: The cardinality of a set is a measure of the number of elements in the set. For…

Q: 1. Give at least 5 pairs of numbers a and b. For each of those pairs find at least 10 elements of…

A: We need to find at least 5 pairs of numbers a and b. For each of those pairs  at least 10 elements…

Q: d) The set E = (-1,0) U (0, 1] is an open set. %3D

A: Given set is E = (-1, 0) ∪ (0, 1]

Q: 2.) Suppose A is a set with 4 elements and B is a set with 3 elements. How many relations are there…

A:

Q: Prove: If A, B and C are sets then AU(BOC) and ((C- (AUB)) (B- (AUC))) are disjoint sets.

A: Let A, B, and C are sets. Now we prove that A∪B∩C and C-A∪B∪(B-(A∪C)) are disjoint.

Q: 8. Let A, B and C be sets. (a) Suppose that AC B and BC C. Does this mean that A S C? Prove your…

A:

Q: Let A and B be sets with P(A) = P(B). Write a proof by contradiction to establish that A = B. [Note:…

A: Let A and B be sets with P(A) = P(B). Write a proof by contradiction to establish that A = B. [Note:…

Q: VII.1. Describe the set (R × Z) ∩ (Z × R)

A: We have to describe the set (R × Z) ∩ (Z × R).

Q: 5. Prove, if true, that if A, B and C are sets that A - (Bn C) = (A - B) U (A - C). If it is not…

A:

Q: Find the closure of each of the following sets: mod T d (a) (3,5) U {6} (b) (-∞, 0) U (0, 1)

A: Given: (a) 3, 5∪6     b -∞, 0∪0, 1 To find: Closure of the given set.

Q: 4. Which of the following pairs of sets are equivalent or equal? (a) A = {x : x € N, x < 6} B = {x :…

A:

Q: How do we denote the empty or null set?

A: A set is said to be an empty set or a null set if there is no element in it.