Question

H Do the 2 things respectively with the three syllogistic arguments given below: 1. Translate the following arguments by using predicate letters (as defined below), constant variables, and quantifiers; and 2. Show that they are logically valid by deriving the conclusion from the premises. {10) [17] PI: P2: C: All humans have inviolable rights. Not all creatures have inviolable rights. Therefore, there are many creatures that cannot be humans. H: being a human 1: having inviolable rights C: being a creature

Answer 1

1. (4x) ( Hoe → Ix) 2. (32) (cx 1 ~ Ix) 1:. (3x) (Cx 1 Hse) 3. Ca A~I a 2, EI 4. Ha :> I a di UI ~ I a 3, Simp. 5. 6 . . ~ Ha 4,5, MT 7. ca 3, Simp. 8. Calata 6, 7, Conj g. (3x) (Cx 1 ~ Hee) 8, EG Hence the argument form is realid.

[18] 1. (7x) (Hx 1~ Mx) 2. ~(73) ( Ax .^ MX) 7. W. (329 (Hx 1 Ax) using rules of quantifiers we can translate the arguments an equivalent form as ts in t. (e) (Hx 7 Mx) 2. (Hx) (Axe + rmx) 1.. (Vx) (Hx-7 Ax) 3. Ha > Ma 1,VT .4. . Aa t...ma 2, UI 5. Mă ~ Aa 4, Trans. 6 Ha N Aa. 3,5, HS 7. (4x) (Hxe + » Aze) 6, UG Hence, the argument form is valid.