Let A = {\bullet ,\square, \bigotimes} and B = {\square,\ominus, \bullet}. (a) List the elements of A X B and B X A. The parentheses and comma in an ordered pair are not necessary in cases such as this where the elements of each set are individual symbol.
(b) Identifiy the intersection of A X B and B X A, for the case above, and then guess at a general rule for the intersection of A µ B and B µ A. where A and B are any two sets.

(a) With A = {•, □, ⊗} and B = {□, ⊖, •}, we have

A × B = {(•, □), (•, ⊖), (•, •), (□, □), (□, ⊖), (□, •), (⊗, □), (⊗, ⊖), (⊗, •)}

and

B × A = {(□, •), (□, □), (□, ⊗), (⊖, •), (⊖, □), (⊖, ⊗), (•, •), (•, □), (•, ⊗)}

(b) The intersection of the two sets above is

(A × B) ∩ (B × A) = {(•, •), (•, □), (□, •), (□, □)}

Not sure what µ is supposed to represent, but I suppose you meant to again write × as in the Cartesian product. By definition, for any two sets A and B, we have

A × B = {(a, b) | a ∈ A and b ∈ B}

Then

(A × B) ∩ (B × A) = {(a, b) | a ∈ A ∩ B and b ∈ A ∩ B}

In the product found above, notice that • and □ are both elements of A and B, while ⊗ and ⊖ are exclusive to either set.

solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw   congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.