# Thread: Is this correct? (It deals with A x B x C stuff)

1. ## Is this correct? (It deals with A x B x C stuff)

Q: Let A = {a, b, c}, B = {x, y}, and C = {0, 1}. Find:
a.) A x B x C
b.) C x B x A
c.) C x A x B
d.) B x B x B

a.) A x B x C = [{a, x, 0}, {a, y, 1}, {b, x, 0}, {b, y, 1}, {c, x, 0}, {c, y, 1}]
b.) C x B x A = [{0, x, a}, {0, x, b}, {0, x, c}, {1, y, a}, {1, y, b}, {1, y, c}]
c.) C x A x B = [{0, a, x}, {0, b, x}, {0, c, x}, {1, a, y}, {1, b, y}, {1, c, y}]
d.) B x B x B = [{x, x, x}, {x, x, y}, {x, y, x}, {y, y, y}, {y, y, x}, {y, x, y}]

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2. Originally Posted by Grillakis
Q: Let A = {a, b, c}, B = {x, y}, and C = {0, 1}. Find:
a.) A x B x C
b.) C x B x A
c.) C x A x B
d.) B x B x B

a.) A x B x C = [{a, x, 0}, {a, y, 1}, {b, x, 0}, {b, y, 1}, {c, x, 0}, {c, y, 1}]
b.) C x B x A = [{0, x, a}, {0, x, b}, {0, x, c}, {1, y, a}, {1, y, b}, {1, y, c}]
c.) C x A x B = [{0, a, x}, {0, b, x}, {0, c, x}, {1, a, y}, {1, b, y}, {1, c, y}]
d.) B x B x B = [{x, x, x}, {x, x, y}, {x, y, x}, {y, y, y}, {y, y, x}, {y, x, y}]

__________
Well a isn't right.

$A \times B \times C = \bigg\{(f,g,h) | f \in A, g \in B, h \in C\bigg\}$

Now, I see no element (a,x,1) in your first set, and that satisfies the conditions. You are correct with what you have, but just not complete.

3. Originally Posted by Mush
Well a isn't right.

$A \times B \times C = \bigg{(f,g,h) | f \in A, g \in B, h \in C\bigg}$

Now, I see no element (a,x,1) in your first set, and that satisfies the conditions. You are correct with what you have, but just not complete.
How about now Mush ( is everything correct now):

A x B x C = [{a, x, 0}, {a, x, 1}, {a, y, 0}, {a, y, 1}, {b, x, 0}, {b, x, 1},
{b, y, 0}, {b, y, 1}, {c, x, 0},
{c, x, 1}, {c, y, 0}, {c, y, 1}]

C x B x A = [{0, x, a}, {0, x, b}, {0, x, c}, {1, y, a}, {1, y, b}, {1, y, c}]

C x A x B = [{0, a, x}, {0, b, x}, {0, c, x}, {1, a, y}, {1, b, y}, {1, c, y}]

B x B x B = [{x, x, x}, {x, x, y}, {x, y, x}, {y, y, y}, {y, y, x}, {y, x, y}]

4. Originally Posted by Grillakis
How about now Mush ( is everything correct now):

A x B x C = [{a, x, 0}, {a, x, 1}, {a, y, 0}, {a, y, 1}, {b, x, 0}, {b, x, 1},
{b, y, 0}, {b, y, 1}, {c, x, 0},
{c, x, 1}, {c, y, 0}, {c, y, 1}]

C x B x A = [{0, x, a}, {0, x, b}, {0, x, c}, {1, y, a}, {1, y, b}, {1, y, c}]

C x A x B = [{0, a, x}, {0, b, x}, {0, c, x}, {1, a, y}, {1, b, y}, {1, c, y}]

B x B x B = [{x, x, x}, {x, x, y}, {x, y, x}, {y, y, y}, {y, y, x}, {y, x, y}]
a) is now complete.
b) is not complete, for example, (1,x,c) is not there.
c) is not complete, for example, (0,a,y) is not there.
d) is not complete, for example, (x,y,y) is not there.

Hint: a), b) and c) should have the same number of elements. d) should have 8 elements.

PS your notation is wrong. Your sets A x B x C should be sets of ordered-3tuples, not sets of sets! Curly brackets denote sets, normal brackets denote ordered n-tuples:

a) should be:

$A \times B \times C = \bigg\{(a, x, 0), (a, x, 1), (a, y, 0), (a, y, 1), (b, x, 0),$ $(b, x, 1),
(b, y, 0), (b, y, 1), (c, x, 0),(c, x, 1), (c, y, 0), (c, y, 1)\bigg\}$

5. Originally Posted by Mush
a) is now complete.
b) is not complete, for example, (1,x,c) is not there.
c) is not complete, for example, (0,a,y) is not there.
d) is not complete, for example, (x,y,y) is not there.

Hint: a), b) and c) should have the same number of elements. d) should have 8 elements.

PS your notation is wrong. Your sets A x B x C should be sets of ordered-3tuples, not sets of sets! Curly brackets denote sets, normal brackets denote ordered n-tuples:

a) should be:

$A \times B \times C = \bigg\{(a, x, 0), (a, x, 1), (a, y, 0), (a, y, 1), (b, x, 0),$ $(b, x, 1),
(b, y, 0), (b, y, 1), (c, x, 0),(c, x, 1), (c, y, 0), (c, y, 1)\bigg\}$

Mush, hopefully 3rd times a charm:

A x B x C = {(a, x, 0), (a, x, 1), (a, y, 0), (a, y, 1), (b, x, 0), (b, x, 1), (b, y, 0),
(b, y, 1), (c, x, 0),
(c, x, 1), (c, y, 0), (c, y, 1)}

C x B x A = {(0, x, a), (0, x, b), (0, x, c), (1, x, a), (1, x, b), (1, x, c), (0, y, a),

(0, y, b), (0, y, c), (1, y, a), (1, y, b), (1, y, c)}

C x A x B = {(0, a, x), (0, b, x), (0, c, x), (1, a, x), (1, b, x), (1, c, x), (0, a, y),
(0, b, y), (0, c, y),
(1, a, y), (1, b, y), (1, c, y)}

B x B x B = {(x, x, x), (x, x, y), (x, y, x), (x, y, y), (y, y, y), (y, y, x), (y, x, y),
(y, y, x)}

6. Originally Posted by Grillakis
Mush, hopefully 3rd times a charm:

A x B x C = {(a, x, 0), (a, x, 1), (a, y, 0), (a, y, 1), (b, x, 0), (b, x, 1), (b, y, 0),
(b, y, 1), (c, x, 0),
(c, x, 1), (c, y, 0), (c, y, 1)}

C x B x A = {(0, x, a), (0, x, b), (0, x, c), (1, x, a), (1, x, b), (1, x, c), (0, y, a),

(0, y, b), (0, y, c), (1, y, a), (1, y, b), (1, y, c)}

C x A x B = {(0, a, x), (0, b, x), (0, c, x), (1, a, x), (1, b, x), (1, c, x), (0, a, y),
(0, b, y), (0, c, y),
(1, a, y), (1, b, y), (1, c, y)}

B x B x B = {(x, x, x), (x, x, y), (x, y, x), (x, y, y), (y, y, y), (y, y, x), (y, x, y),
(y, y, x)}
You put (y,y,x) in twice on the last one, and missed out (y,x,x). Apart from that, it's perfect.

7. Originally Posted by Mush
You put (y,y,x) in twice on the last one, and missed out (y,x,x). Apart from that, it's perfect.
lol...thanks mush

8. The first thing you should have thought: Since A has 3 members and B and C both have 2, A X B X C, B X C X A, and C X A X B will have 3(2)(2)= 12 members while B X B X B will have 2(2)(2)= 8 members.

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# if A= {a,b,c}, B={x,y} find A×B, B×A, B×A, B×B

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