To make a valid deduction with a Quantifier Statement and a Sufficient & Necessary statement, the variable the statements have in common must be the sufficient condition in the Sufficient & Necessary condition.
Our two premises here are:
P: B âž¡ X
P: M-some-B
What variable do these share in common? B.
Is B the sufficient condition? Yes! So we can combine these statements to make a valid deduction as follows:
M-some-B âž¡ X
To conclude:
M-some-X
This must be true. If some Ms are Bs, this means at least one M is a B.
And since every B is an X, we know that at least one M is also an X.
Hope this helps! For a more in-depth review of these concepts, check out our lesson on Quantifiers.
