Show that each of these conditional statements is a tautology using logical equivalences.a) (𝑝 ∧ 𝑞) → 𝑝b) ¬𝑝 → (𝑝 → 𝑞)c) (𝑝 ∧ 𝑞) → (𝑝 → 𝑞)

Show that each of these conditional statements is a tautology using logical equivalences.a) (𝑝 ∧ 𝑞) → 𝑝b) ¬𝑝 → (𝑝 → 𝑞)c) (𝑝 ∧ 𝑞) → (𝑝 → 𝑞)

Show that ¬(𝑝 ∨ (¬𝑝 ∧ 𝑞)) and ¬𝑝 ∧ ¬𝑞 are logically equivalent by:a) Using a truth table (3 POINTS)b) Using logical equivalences

If 𝑥 = 7 − 4√3, then the value of √𝑥 + 1√𝑥 :(ii) Prove that :(𝑥𝑞+1𝑥𝑝+1)𝑞+𝑝. (𝑥𝑟+1𝑥𝑞+1)𝑟+𝑞. (𝑥𝑝+1𝑥𝑟+1 )𝑝+𝑟= 1

Given that 𝑝=3, 𝑞=−1 and 𝑟=11, choose the two answer options containing expressions of equal value.A2⁢𝑝⁢𝑞⁢𝑟B4⁢𝑝+𝑟⁢𝑞C𝑟+2⁢𝑞D𝑝⁢𝑟𝑞E3⁢𝑝

Calculate the solution to these simultaneous equations using the elimination method: (1)(1)5𝑝+𝑞5p+q==1313 (2)(2)𝑝−𝑞p−q==55