The compound statements s_1 = p and (q or r) and the statement s_2 - (p and q) o

Question

The compound statements s_1 = p and (q or r) and the statement s_2 - (p and q) or r are not equivalent. Find truth values for each of p, q and r that make s_1 false and s_2 true: p: _____ q: ______ r: _______ Let Q be a quadrilateral (four-sided figure in the plane) and consider the statement: If Q is a square, then Q is a parallelogram and all sides of Q have equal length Write out in English the following statements associated with (*), and use De Morgan's Law if possible. a) The converse. b) The contrapositive. c) The inverse. d) Consider a compound statement with logical structure s rightarrow (p and q), where each of s, p and q an each take on both truth values, T and F, leading to eight cases. i) Find truth values for s, p and q that make the statement s rightarrow (p and q) false. p: _____ q: ______ r: ______ ii) Note that the particular statement (*) above has logical structure s rightarrow (p and q) where s stands for "Q is a square": p stands for "Q is a parallelogram": and q stands for all side of Q have equal length." Can these statements s, p and q take on the true values in your answer to part i)? Y/N______ iii) What is the name given to a parallelogram all of whose sides have equal length? _______

Explanation / Answer

s1 = p ^ (q v r)
s2 = (p ^ q) v r
we are to find truth values of p,q and r that will make s1 false and s2 true:
To make s1 false:
1) p can be false and q & r can be anything or
2) q and r both are false and p can be anything

To make s2 true:
1) r can be true and p,q can be anything
2) p and q can be true and r can be anything;
Thus, possible outcomes for p,q,r are : F T T & F,F,T respectively;

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.