Give a proof of
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- Prove that (p →(q →r)) → ((p →q) →(p →r)) ≡ T for all propositions p, q, r.For P= 0 and compute the value of K under the condition. if (P <= 1) K = P + 5else if (P > 1 && P <= 5) K = P + 3else if (P > 8) K= P - 1else K = PUse Direct Proof to prove this.. If x ∈ ℝ and x 2 + x + 6 < 0, then -x 2 + 2x - 9 < 0.
- Show that p ↔ q is logically equivalent to (p ∧ q) ∨ (¬p ∧¬q).Prove that it is logically equal using common equivalent proposition. 1. ¬[p v (¬p ˄ q) ≡ (¬p ˄ ¬q) 2. p → (q ˄ ¬r)Compute the gradient with respect to all parameters of f(w0 + w1a1 + w2a2) when w0 = 3, w1 = −2, a1 = 2, w2 = −1, a2 = 4, and β = 0.25 using backpropagation