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Prove the following sequents. [50 points]
a. (a ʌ b) ʌ c ͱ a ʌ (b ʌ c)
b. p ͱ q → (p ʌ q)
c. (p → q) ʌ (q → r) ͱ p ʌ q → r
d. p → (q ʌ r) ͱ (p → q) ʌ (p → r)

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Prove the following sequents. [50 points]
a. (a ʌ b) ʌ c ͱ a ʌ (b ʌ c)
b. p ͱ q → (p ʌ q...
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