Logic Worksheet With Answers Page 3
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22The statements diagonally opposite each other are negations.
All A are B
No A are B.
(There are no A that are no B)
(All A are not B)
Some A are B
Some A are not B
(There is at least one A that is in
(Not all A are B)
B)
Here are some examples of quantified statements:
Symbolically, the universal statement “All A are B” can be written as “ A are B”, or “ A
B”.
The existential statement “Some A are B” can be written as “
so that
”
Ex: The mechanic told me, “All piston rings were replaced.” I later learned that the mechanic
never tells the truth. What can we conclude?
Because the mechanic never tells the truth, we can Conclude that the truth is the negation of what
I was told.
The negation of “All A are B” is “Some A are not B”. Thus, I can conclude that
Some piston rings were not replaced.
I can also correctly conclude that:
At least one piston ring was not replaced.
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