Question
Match the phrase to the correct logical statement.Converse_ 9-pInverse P-~qContrapositive, q--pBiconditional, p+qNegate both Gndi Ifnotp then notqInterchongeInegaleIfnot hen notp:InterchangeIfq Ihen pConnectVth"only ifonly ifq:
Match the phrase to the correct logical statement. Converse_ 9-p Inverse P-~q Contrapositive, q--p Biconditional, p+q Negate both Gndi Ifnotp then notq Interchonge Inegale Ifnot hen notp: Interchange Ifq Ihen p Connect Vth" only if only ifq:
Answers
For each given statement, write (a) the converse, (b) the inverse, and (c) the contrapositive in if . . . then form. In some of the exercises, it may be helpful to restate the statement in if . . . then form.
$p \rightarrow(q \vee r)$ (Hint: Use one of De Morgan's Laws as necessary.)
Services are original statement. So for part A, we want our converts. So that is our consequent first, which is the negation of Q implies Pete, you know, for inverse we want delegation off. P implies a negation of the negation of cute, and that is just cute. So we have a negation of P implies Q. Unless they we have our country positive, so Contra positive is our consequence. It's negation. So delegation of the Nation of Q implies the negation of Pete, so that's equal to que implies negation of Pete. So we get the following.
They said. We have the following statement and we want our converse. That is our decedent, or are consequence implies are anti feeding. In this case, it's p implies our or litigation of cute and for part b wants are invests for inverse is our negation of our antioxidant. So that's navigation off. Our organization of Q implies navigation of our consequence, which is so now let's explain its found this. So we get the negation of far and kill implies litigation a peak. Lastly, we have our contra positive. So we just saw 12 are and he ceded and consequence in our inverse. So we have indication of P implies Gatien of our and you.
Okay, so we're giving the following conditional statement. So we have. And if that statement so that is that's lets the following the exit is ahead, BP, and that's that. I don't see it pick you. So we have that p implies cute. And now, for part, a were asked to find the converse, which is si que implies p. Okay, so we have Q, That is I don't see it. Actually, we need to have an if then statement again. We have I don't see it. Then we have p, which is the exit is ahead. I get an offer, Part B. We want our in verse. And that is, um Let's see you. All right. That in green are in verse is the negation of P implies the negation of cute. Okay, so let's start with if and then we have the negation of P. That is the exit is not ahead. And then we have then the negation of Q, which is I do see it forget and lastly report See, we want the contra positive. So that is, um let's see the negation of que implies the negation of people. Okay, So start by putting an If so, I have if and then one against them and after interrogation. Q. So Q is I don't see it. So delegation of Q is, If I do see it, then we have a negation of Peak is the exit is not ahead. Okay, so there we go.
Okay, so we're asked to find the converse for our following statement. So let's let the negation of Q A implies vindication of P, which is beat. So the converse is be implies. A, which is B is the negation off p implies negation of cute. Okay, And now, for part B, we want our interests. So that is the negation of a implies the negation of beat. Okay, so let's write that out. We have a which is the negation of Q, and we want the negation of that that implies the negation of B, which is negation of people. So we get que implies Pete. And now for see, we want the culture positive. So we have a negation of be employees indication of a so yet dedication of being, which is a delegation of p, implies delegation of A, which is indication of cute. So we get P implies Q