How many one-to-one correspondences are there between two sets with 6 elements each?
2 answers:
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Answer:
Step-by-step explanation:
<span>A(2, -2), B(4, -2), C(1, -3), D(5, -3).
A'(1, 2), B'(1, 4), C'(2, 1), D'(2, 5)
That looks like a rotation 90 degrees around the origin then a translation.
Let's do the rotation ABCD->A"B"C"D"
The rotation is (x,y)->(-y,x)
</span>A"(2, 2), B"(2,4), C"(3,1), D"(3,5).
Compare to
A'(1, 2), B'(1, 4), C'(2, 1), D'(2, 5)
we need to translate one unit to the left.
Answer: 90 degree rotation around the origin then translation by (-1,0)
A'(1, 2), B'(1, 4), C'(2, 1), D'(2, 5)
That looks like a rotation 90 degrees around the origin then a translation.
Let's do the rotation ABCD->A"B"C"D"
The rotation is (x,y)->(-y,x)
</span>A"(2, 2), B"(2,4), C"(3,1), D"(3,5).
Compare to
A'(1, 2), B'(1, 4), C'(2, 1), D'(2, 5)
we need to translate one unit to the left.
Answer: 90 degree rotation around the origin then translation by (-1,0)