Select the mistake that is made in the proof given below. Theorem. For any two integers, x and
y, if 3 divides x and 3 divides y, then 3 also divides x+2y. Proof. Since 3 divides x,x=3k for
some integer k. Since 3 divides y,y=3k for some integer k. Plugging in the expression 3k for x
and 3k for y into x+2y gives x+2y=3k+2(3k)=3k+6k=9k=3(3k) Since k is an integer, 3k is also
an integer. Since x+2y=3m, where m=3k is an integer, 3 divides x+2y. Failure to properly
introduce variable. Generalizing from examples. Assuming facts that have not yet been proven.
Misuse of existential instantiation..
Select the mistake that is made in the proof given below. Theorem. Fo.pdf
1. Select the mistake that is made in the proof given below. Theorem. For any two integers, x and
y, if 3 divides x and 3 divides y, then 3 also divides x+2y. Proof. Since 3 divides x,x=3k for
some integer k. Since 3 divides y,y=3k for some integer k. Plugging in the expression 3k for x
and 3k for y into x+2y gives x+2y=3k+2(3k)=3k+6k=9k=3(3k) Since k is an integer, 3k is also
an integer. Since x+2y=3m, where m=3k is an integer, 3 divides x+2y. Failure to properly
introduce variable. Generalizing from examples. Assuming facts that have not yet been proven.
Misuse of existential instantiation.
