Quantifier Rules

Question 1

Some

Answer 1

At least one, could be all.

ie; Some animals are bears (Animals -some- Bears)

Question 2

Reversal of Some

Answer 2

Directly reversible. The reversal of some is also some.

ie; Animals -some- Bears
Reversal: Bears -some- Animals

Question 3

Most

Answer 3

More than half, at least 50.1%

ie; Most SCOTUS Justices graduated from Harvard (SCOTUS Justice -most- Harvard Grad)

Question 4

Reversal of Most

Answer 4

Not directly reversible. The reversal of most is some.

ie; SCOTUS Justice -most- Harvard Grad
Reversal: Harvard Grad -some- SCOTUS Justices

Question 5

All

Answer 5

Every single one.

ie; All humans are animals (Human –> Animal)

Question 6

Reversal of All

Answer 6

Not directly reversible. The reversal of all is some.

ie; Human –> Animal
Reversal: Animal -some- Human

Question 7

Valid Deductions/Conclusions With Quantifiers

Rule #1

Answer 7

Premises MUST contain a sufficient and necessary condition.

ie; A –> B

Question 8

Exception to Quantifier Deductions/Conclusion Rule #1

Answer 8

Premises contain at least TWO most statements with the LEFT side in common.

ie; A -most- B
A -most- C
Con: B -some- C

Question 9

Valid Deductions/Conclusions With Quantifiers

Rule #2

Answer 9

Premises MUST have a sufficient condition in common. The sufficient of the conditional statement must match the RIGHT side of the quantifier statement.
ie; A -some- B
B ——–> C
Con: A -some- C

The arrow in the deduction chain must point AWAY from the some statement.
ie; A -some- B —> C
Con: A -some- C