Answer the following true or false. justify your answer.
(a) if a is a subset of b, and x∈b, then x∈a.
(b) the set {(x, y) ∈ r2 | x > 0 and x < 0} is empty.
(c) if a and b are square matrices, then ab is also square.
(d) a and b are subsets of a set s, then a∩b and a∪b are also subsets of s.
(e) for a matrix a, we define a^2 = aa.

a) False

b) True

c) True

d) True

e) True

Step-by-step explanation:

a) Consider the sets and . Observe that A is a subset of B and but

b) Any number different of 0 can be positive and negative simultaneusly. Then doesn't exist such that . Then the set is empty.

c) If the multiplication AB is defined and A and B are square matrices with A of size nxn, then B is the size nxn and the matrix AB is the size nxn.

d) Let A and B subsets of a set S. Since each element of A and B are in S then each element of is in S. Also, if , the and then . This shows that .

e) By definition AA=A^2

the 2 figures are congruent bc if you reflect abcd over the y axis then over the d axis the figures overlap

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