For logic Taking the universe of discourse to be the set {1, 2, 3}, specify extensions for “F”, “G”, and “H” that make the following schemata true: (a) (∃x)(Fx≡Gx) • ~(∀x) (Fx ⊃ Gx) • (∀x)(Gx ⊃ Fx) (b) (∀x)(Fx • Gx ⊃ Hx) • (∀x)(Fx ⊃ Gx • Hx) • (∀x) (Gx ⊃ Fx • Hx)

4. Suppose that the variable x represents people, and F(x): "x is friendly" T(x): "x is tall" A(x): "x is angry". Express each of the following statements using these predicates, quantifiers, and logical connectives. (a) Some people are not angry. (b) All tall people are friendly. (c) No friendly people are angry.

Just B please

4. Translate the following sentences from English to predicate logic. The domain that you are working over is X, the set of people. You may use the functions S(x), meaning that " x has been a student of 6.042," A(x) meaning that "x has gotten an 'A' in 6.042," T(x) meaning that "x is a TA of 6.042," and E (x, y) meaning that "x and y are the same person." (i) There are people who have taken 6.042 and have gotten A's in 6.042. (ii) All people who are 6.042 TA's and have taken 6.042 got A's in 6.042. (iii)There are no people who are 6.042 TA's who did not get A's in 6.042.