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1. Let M be the PDA with states Q = {q0, q1, and q2}, final states F = {q1, q2} and transition function
δ(q0, a, λ) = {[q0, A]}
δ(q0, λ , λ) = {[q1, λ]}
δ(q0, b, A) = {[q2, λ ]}
δ(q1, λ , A) = {[q1, λ ]}
δ(q2, b, A) = {[q2, λ ]}
δ(q2, λ , A) = {[q2, λ ]}(a) Draw the state diagram for M.
(b) Using set notation, describe the language accepted by M.
(c) Trade a computation of the word aaaabb.
ABCD is a rectangle. Δ ADE and Δ ABF are two triangles such that ∠E=∠F as shown in the figure. Prove that AD x AF=AE x AB. Ans: Consider Δ ADE and Δ ABF ∠D = ∠B
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