Answer
a. Statement (1) is true. Statement (2) is false.
b. Statement (1) is true. Statement (2) is false.
Work Step by Step
a. Statement (1) says that no matter what square anyone might give you, you can find a triangle of a different color. This is true because the only squares are e, g, h, and j, and given squares g and h, which are gray, you could take triangle d, which is black; given square e, which is black, you could take either triangle f or i, which are gray; and given square j, which is blue, you could take either triangle f or h,
which are gray, or triangle d, which is black.
a. Statement (2) says that you must find a triangle so that no matter what square anyone might give you, your triangle will have a different color. This statement is false because triangles only come in two colors black and gray. Squares come in three colors: black, gray, and blue. Hence no matter which triangle we choose, someone can find a square with a matching color.
b. Statement (1) says no matter what circle anyone might give you, you can find a square of the same color. This is true. The set of circles is: {a, b, c}. The set of squares is: {e, g, h, j}. If someone gives you circle a or c (which are both blue), you can counter with square j (which is also blue). If someone gives you circle b (which is gray), you can counter with square g or h (which are both gray).
c. Statement (2) says you must find a square so that no matter what circle anyone might give you, your square will have the same color. This is false because circles come in two colors: blue and gray. It is not possible to find one square that has the same color as any circle someone may choose. (This statement would be true if circles came in only one color and there is a square of that color, which would be the square that you choose).
