If statement forms P and Q are logically equivalent, then P ↔ Q is a tautology. Conversely, if P ↔ Q is a tautology, then P and Q are logically equivalent. Use ↔ to convert each of the logical equivalences in 29–31 to a tautology. Then use a truth table to verify each tautology. 29. p → (q ∨ r) ≡ (p ∧ ∼q) → r

answer is 12345678900987654321234567890987654321

step-by-step explanation:

step-by-step explanation: 2

-3 degrees

step-by-step explanation:

place r′ so that qr′ is parallel to the tangent.

now we get that ∠r′py=∠pr′q, where y is on the tangent, on the opposite side of p from x.

also, because of the symmetry, ∠r′py=∠qpx.

finally, note that no matter where we place r, as long as it's on the correct arc, we have ∠prq=∠pr′q.

stringing all these equalities together, we end up with ∠prq=∠qpx.

this picture will show how its going to look like.

hope this by jack monhen