The following valid arguments come in pairs. The validity of the first of the pair makes crucial use of the meanings of the blocks language predicates, whereas the second adds one or more premises, making the result a first-order valid argument. For the latter, give a proof that does not make use of Ana Con. For the former, give a proof that uses Ana Con but only where the premises and conclusions of the citation are literals (including 1). You may use Taut Con but do not use FO Con in any of the proofs. 13.32 13.33 3x (Tet(x) A Small(x)) 1x [Tet(x) + (Large(x) v Medium(x))] 3x (Tet(x) A Small(x)) Vy (Small(y) v Medium(y) V Large(y)) Vx Tet(x) + (Large(x) V Medium(x))] 13.34 13.35 Vx (Dodec(x) + SameCol(x, a)) SameCola, c) Vx (Dodec(x) +SameCol(x, c)) Vx (Dodec(x) + SameCol(x, a)) SameCola, c) Vx Vy Vz (SameCol(x, y) A SameColly, z)) + SameCol(x, z)) Vx (Dodec(x) + SameCol(x, c))

Cone w has a radius of 8 cm and a height of 5 cm. square pyramid x has the same base area and height as cone w. paul and manuel disagree on how the volumes of cone w and square pyramid x are related. examine their arguments. which statement explains whose argument is correct and why? paul manuel the volume of square pyramid x is equal to the volume of cone w. this can be proven by finding the base area and volume of cone w, along with the volume of square pyramid x. the base area of cone w is π(r2) = π(82) = 200.96 cm2. the volume of cone w is one third(area of base)(h) = one third third(200.96)(5) = 334.93 cm3. the volume of square pyramid x is one third(area of base)(h) = one third(200.96)(5) = 334.93 cm3. the volume of square pyramid x is three times the volume of cone w. this can be proven by finding the base area and volume of cone w, along with the volume of square pyramid x. the base area of cone w is π(r2) = π(82) = 200.96 cm2. the volume of cone w is one third(area of base)(h) = one third(200.96)(5) = 334.93 cm3. the volume of square pyramid x is (area of base)(h) = (200.96)(5) = 1,004.8 cm3. paul's argument is correct; manuel used the incorrect formula to find the volume of square pyramid x. paul's argument is correct; manuel used the incorrect base area to find the volume of square pyramid x. manuel's argument is correct; paul used the incorrect formula to find the volume of square pyramid x. manuel's argument is correct; paul used the incorrect base area to find the volume of square pyramid x.