How many attributes pieces should be on the desk for each description? (DISCRETE MATH)?

Question

Set of attributes pieces are often found in elementary classrooms. One common set consists 32 pieces. There are 8 pieces for each color: red, blue, yellow and green. For each color there are 4 diff. shapes: square, circle, rhombus and triangle. For each shape and color, there are two sizes: large and small.

A set of attribute is given to each student, and each student is asked to place pieces that satisfy certain criteria on his or her desk.

How many attributes pieces should be on the desk for each description?

a. Large and yellow
b. Red or yellow
c. Green or small
d. square and triangle
e. circle or square
f. circle and green, or yellow

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Answer 1

There are 8 yellow pieces. Of these half are large and half are small. So 4.

There are 8 yellow pieces and 8 red pieces, so 16.

There are 8 green pieces. There are 16 small pieces. However, 4 pieces are both small and green. So 8 + 16 - 4 = 20.

There are 8 triangles. There are 8 squares. However, no triangles are squares, so 0.

There are 8 circles. There are 8 squares. So 16.

There are 8 circles. Two of them are green. There are 8 yellow pieces. So 8 + 2 = 10.

Answer 2

-------------R------------B-------------------Y------------------G
-------------8-------------8-------------------8------------------8
-------_______----_______-------________-------________
-------|---|----|---|----|----|----|----|------|----|---|----|-------|----|----|----|
------S--C--R--T---S--C--R---T----S--C--R---T---- S--C--R---T
------|-|--|-|--|-|--|-|---|-|--|-|--|-|--|-|-----|-|--|-|--|-|--|-|------|-|--|-|--|-|--|-|
-----s l-s l-s l-s l--s l--s l--s l-s l----s l-s l-s l-s l------s l-s l-s l-s l

if you make a matrix like this you can figure out things very easily S-SQUARE, C-CIRCLE, R-RHOMBUS, T-TRIANGLE,
R-RED, G-GREEN, B-BLUE, Y-YELLOW, s-small, l-large

a) large and yellow = count l's which are Y = 4
b) red or yellow = count R's and count Y's = 8 + 8 = 16
c) green or small = count G's and count s's which are not G's since G's which are small have been counted = 8 + 12 = 20
d) square and triangle = no squares are triangles = 0
e) circle or square = count C's and Count S's = 2+2 + 2+2 + 2+2 + 2+2 = 16
f) circle and green, or yellow = count C's which are G's and Y's = 2 + 8 = 10

I cannot display the matrix in the space provided. I think if you could provide me an email I can send you the same as attachment