Conditional Propositions

Restate the following in the form of if p than q.

  1. Joey will pass the Discrete Structure Exam if he studies hard.
  2. A neccessary condition for Fernando to buy a computer is that he obtains $2000.
  3. A sufficient condition for Katrina to take the Algorithm course is that she passes
    Discrete Structures.
  4. You may inspect the aircraft only if you have the proper security clearance.

Assume that p and r are false and q and s are true.
Find the truth value of each proposition below.

  1. (p->q)^(q->r)
  2. (s->(p ^ ~r))^((p->(r v q))^s)

Assume that p is true, q is false, and r's status is unknown at this time.
Can the statement below to be true, or false, or unknown?

  1. (q v r) if and only if r

Determine the truth value of each proposition below.

  1. If 3+5<2, then 1+3 = 4
  2. If 3+5>2, then 1+3 != 4
  3. 3+5<2 if and only if 1+3 != 4