Let S1, S2, S3 be convex sets. Is their intersection nS, necessarily a convex set If 'yes' show, if 'no' argue why?

Q: . If A and B are sets in a universal set U, then AUB=AnB.

A: We proved this by wave diagram

Q: Express the following sets in the simplest way possible. If needed, use 'set builder notations'. Do…

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Q: 1. example of sets A and B for which A B but Ag B.

A: Cardinality of a set is number of elements in the set.

Q: 4. Prove that if A and B are convex sets, then AN B is also convex.

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Q: Please fill in the blank. (2 pts, 0.5pt each, due in lab) a. Si S2 = {-3, 1, 4} b. S1'| × |S2| = c.…

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

Q: 2. Consider the following statement: "if A, B are two non-empty sets, each one having a minimum,…

A: Let, mA = min {x : x ∈ A}        mB = min {x : x ∈ B}   Now, let m = min{mA , mB} Then, m = mA if mA…

Q: What can you say about the sets A and B if AB=A?

A: Consider two sets A  and B. Then the symmetric difference between these two sets is denoted by A⊕B.…

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.

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Q: Suppose that you have two sets, and you know that both sets are convex. Proven that the intersection…

A: convex set is a set of points such that, given any two points x,y in that set, the straight line…

Q: use a Venn diagram to determine which relationship, C, =, or 2, is true for the pair of sets. AUB,…

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Q: True or false 1.The intersection of two sets is the set of all the equal elements that belong to…

A: Since you have not mentioned the questions to be solved, so we are providing you solutions for first…

Q: (b) Let={A i EN} be a family of sets with A₁ CA₂ CCA10 C... Prove that nA = A₁.

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Q: 16. If A, B and C are sets, then Ax (BUC)= (A x B)U(AXC).

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Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.