Math (Sets) Exaam 2025/2026 Questions With Completed & Verified Solutions.

Math (Sets)

2^n - ANS -The # of subsets
\A set can be defined by what 3 ways? - ANS -1.) by giving a verbal description 2.) by listing. 3.)
by using set builder notation
\A^ 1 ( What is the compliment of A) - ANS -The set of all x such that x belongs to the universe
and x doesnt belong to A { X l X E U and X E A}
\Commutative Laws - ANS -AnB= bnA & AUB = BUA
\Distributive Laws - ANS -AN(BUC) = (AnB)U(ANC) & AU(BnC) = (AUB)n (AUC)
\how can you show the empty set? - ANS -a circle with a line through it or empty brackets
\If 2 equal sets are equivalent the.. 2 equivalent sets... - ANS -may not be equal
\N(A) = ? - ANS -the number of elements in set A , the cardinal number
\What are inequalities? - ANS -If A & B are finite sets, A has fewer elements than B.
\what is a 1 to 1 correspondence? - ANS -If the elements of set A and set B can be paired so
that for each element of A there is exactly one element of B
\What is a set union? - ANS -The set of all x such that x belongs to A or B or both. {XlX E A or X
E B or X E both A & B)
\what is a set? - ANS -a collection of objects (well defined) called elements
\What is a subset? and whats the symbol? - ANS -A is a subset of B which means every
element in A is also in B. The symbol is similar to and equal or greater than sign but its circular
\What is an ordered pair - ANS -(a,b) a is the 1st component b is the 2nd. (a,b) not equaled to
(b,a)
\What is Associative Laws? - ANS -An(BnC) = (AnB)nC & AU(BUC) = (AUB)UC
\what is Cartesian Product of Sets? - ANS -The set of ordered pairs (x,y) such that x belongs to
set A and y belongs to set B. AXB = { (x,y) l X E A and Y EB}
\What is Demorgan's law? - ANS -(AUB)^1 = A^1 n B^1 & (AnB)^1 = A^1 U B ^1
\What is disjoint? - ANS -What a question is equal to nothing
\What is equivalent sets? - ANS -Can be put into a 1 to 1 correspondence with each other. A
(squiggle sign) B. They have the same # of elements.
\What is set intersection? - ANS -the set of all x such that x belongs to A and x belongs to B.
AnB = { X l X E and X E B }
\what is set theory? - ANS -the basis of all mathematics
\what is the definiton of equal sets - ANS -every element in A is also in B, every element in B is
also in A. Equal sets have the same elements, not necessarily in same order. A=B
\What is the difference of sets? - ANS -The set of all x such that x belongs to a and x doesnt
belong to b. A-B = { X l X E A and X (crossed E) B}
\What is the infinite set? - ANS -A set put into a 1 to 1 correspondence with a proper subset of
itself.
\What is the universe? - ANS -The set of all #'s under consideration. Symbol equals U
\what s a proper subset? - ANS -A is a proper subset of B means that every element in A is also
in B. But there is at least 1 element in B not in A. The symbol is a sideways C
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