# Can someone help me understand how to symbolize?

1. There are jackals on the stairs and in the elevator and Tom is scared.
2. If there are jackals on the stairs, then they are not on the elevator and Mary is happy.
3. Either it is the case that, if there are jackals on the stairs, Bruce is angry or it is the case that if there are wolves in the walls, then there are no jackals on the stairs.
4. Tom is scared if, and only if, there are jackals in the elevator and if, and only if, there are jackals on the stairs.
5. Mary is not happy and Tom is scared, if there are no wolves in the walls. I believe if I had the symbolization, then I could run the truth tables.

• S = Jackals on the stairs
• E = Jackals on the elevator
• T = Tom is scared
• M = Mary is happy
• B = Bruce is angry
• W = Wolves in the walls

1. S & E & T
2. S → (~E & M)
3. (S → B) ∨ (W → ~S)
4. T ↔ (E & S)
5. ~W → (~M & T)

Let J = is a Jackal

Let ST = on the Stairs

Let E = in the Elevator

Let Tom = Tom

Let SC = is Scared

Let Mary = Mary

Let H = is Happy

Let Bruce = Bruce

Let A = is Angry

Let WO = is a wolf

Let WA= in the walls

1. ∃x(Jx ∧ STx) ∧ ∃y(Jy ∧ Ey) ∧ SC(Tom)

2. ∃x(Jx ∧ STx) ⊃ (~∃y(Jy ∧ Ey) ∧ H(Mary))

3. (∃x(Jx ∧ STx) ⊃ A(Bruce)) ∨ (∃x(WOx ∧ WAx) ⊃ ~∃x(Jx ∧ STx))

4. (SC(Tom) ⇔∃y(Jy ∧ Ey)) ∧ (SC(Tom) ⇔ ∃x(Jx ∧ STx))

5. ~∃x(WOx ∧ Wax) ⊃ (~H(Mary) ∧ SC(Tom))

Will somebody else please check this for accuracy?