(Solved): please do these questions please  3. Construct a truth table for each formula below. Which ones ...

3. Construct a truth table for each formula below. Which ones are tautologies? (a) \( (\bar{p} \vee q) \Rightarrow p \) (b) \( (p \Rightarrow q) \vee(p \Rightarrow \bar{q}) \) (c) \( (p \Rightarrow q) \Rightarrow r \) Find the converse, inverse, and contrapositive of these implications. (a) If triangle \( A B C \) is isasceles and contains an angle of 45 degrees, then \( A B C \) is a right triangle. (b) If quadrilateral \( A B C D \) is a square, then it is both a rectangle and a rhombus. (c) If quadrilateral \( A B C D \) has two sides of equal length, then it is either a rectangle or a rhombus. 9. Determine whether the following formulas are true or false: (a) \( \bar{p} \Leftrightarrow q \equiv \bar{p} \Leftrightarrow \bar{q} \) (b) \( (p \Rightarrow q) \vee(p \Rightarrow \bar{q}) \equiv \bar{p} \) (c) \( p \Rightarrow q \equiv q \Rightarrow p \) Which of the following statements are equivalent to the statement "if \( x^{2}>0 \), then \( x>0 \) "? (a) If \( x>0 \), then \( x^{2}>0 \). (b) If \( x \leq 0 \), then \( x^{2} \leq 0 \). (c) If \( x^{2} \leq 0 \), then \( x \leq 0 \). (d) If \( x^{2} \ngtr 0 \), then \( x \ngtr 0 \).