mathematical logic problem?

[stable meteor]

The question requires to prove is that if T or D are true, R is false

Should I use Disjunction Elimination?

[remote adder]

What does $\subset$ mean here?

[tepid trench]

SWR

[stable meteor]

From what i understand from my teacher, he means By ⊂ conditional relations ⇒

[remote adder]

So $\subset$ just means $\Rightarrow
$?

[tepid trench]

SWR

[stable meteor]

Yeah, and my solution is based on that

[remote adder]

What are mp, Ds, Mt, and so on?

[stable meteor]

1 ~ A ⊂ [ A ∨ ( T ⊂ R ) ] imposition

2 ~ R ⊂ [ R ∨ (A ⊂ R) ] imposition

3 (T ∨ D) ⊂ ~ R imposition

4 (A ∨ (T ⊂ R)) ∨ ~ A (DeMorgan's Law)

5 (A ∨ (T ⊂ R)) ⊂ ~ A (Contrapositive)

6 T ⊂ R ⊂ ~ A
(Modus Ponens to (1,5))

7 ~ A ⊂ ~ R (Contrapositive)

8 T ⊂ ~ R (Modus Ponens to(6, 7))

9 (T ∨ D) ⊂ ~ R (Modus Ponens to (3, 8))

[stable meteor]

Mt: modus tollens.
Mp: Modus ponens
Ds: disjunctive syllogism

[zinc valley]

Can you explain the meaning of all your symbols? I'm familiar with "=>" for "implies" and "∈" to me means set containment, as 1 is contained in the set of integers.

What is "/"? Is the picture all the givens?