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And OrProof Techniques/Lemmas Better for cutting and Modus Ponens: From & and &->8, conclude 8_ Deduction: Assume 0, prove B, conclude &~8. paisting ...

Question

And OrProof Techniques/Lemmas Better for cutting and Modus Ponens: From & and &->8, conclude 8_ Deduction: Assume 0, prove B, conclude &~8. paisting Equivalence: From u and >u conclude & iff B. Contrapositive: _8 > 7u iff (a^-8) iff &>8. Transitivity: From & >8 and 8 >Y, conclude 0-Y_ By Cases: From avB, &->Y and 8>Y, conclude Y By Contradiction: From u-B,and U->~B; conclude & _ Inconsistent: From 8 and ~B; conclude anything: Separating

And Or Proof Techniques/Lemmas Better for cutting and Modus Ponens: From & and &->8, conclude 8_ Deduction: Assume 0, prove B, conclude &~8. paisting Equivalence: From u and >u conclude & iff B. Contrapositive: _8 > 7u iff (a^-8) iff &>8. Transitivity: From & >8 and 8 >Y, conclude 0-Y_ By Cases: From avB, &->Y and 8>Y, conclude Y By Contradiction: From u-B,and U->~B; conclude & _ Inconsistent: From 8 and ~B; conclude anything: Separating And: From GAB, conclude & and B. Selecting Or: From uvf and ~0, conclude 8. Eval Building: From 0, &" B; conclude UAU ~(BAy), avy, Y->0, 83= Double Negation: From "U, conclude &. Add or remove at will: Excluded Middle: Uv-a and -(a^-a)_ Commutative: avf iff Bva and &^ iff BAa De Morgan's Law: (anB) iff ~uv-B Distributive: YA(avB) iff (YAa)V(YA8) and Yv(anB) iff (YVa)A(yvB)



Answers

State and give an example of Modus Ponens. Similarly, state and give an example of
Modus Tollens

Hey, it's clear. So when you read here, So we're gonna let an arbitrary statement in the form if P thank you. It can also be not p not cue. Excuse him, then not pee. So the truth tables of these statements, he too, not P, not Q peas and Q not Q. Then not pee True true phones. This would be true this to be true peace. True Falls, falls truth. So the phones, What was this falls true? True falls true and true Zach. Then if P then Q B falls And if negative, if not Q then not people befalls a swell justice delegation symbol. So we see from the truth table that the statement, If you pee, then Q. And if not, Q than not pee are equivalent to one another, so we can transform an arbitrary statement to a statement and pre next, normal for him that is equivalent to the given scene.

You were asked to express the quantification. They're just unique. X p of x introduced infection once before using universal quantification this Sancho pontifications and logical operators. Okay, so we can be right there. Just accept that you bitch! And for all why P of y implies that X is equal to ay right. So if we have to values or if there is some value X, it's that p of X is true and for all why P Y is also true And this implies that X equals y because we wanted to be a unique value. So if it is unique in X equal to y or there is only one values such that it is true.

In this problem we need to state and give examples from modest opponents and modest rolince. So first of all, we have motives, opponents. Now, this is an argument form. The two premises are if he than Q, and P. And then the conclusion will be shoot. Or just consider an example. If he barks, then he is a dog. The next premise needs to be P. So that will be he barks. And then the conclusion should be cute. So the conclusion will be he is a dog. Now let us consider the next one, which is modus Collins. Yeah, the two premises in this case will be F. P. Then Q. And not cute than our conclusion will be not picked. But it's considered an example. Yeah, if he barks okay, then he is a dog, then we have not cute. So that means he is not a dog. So we have the conclusion is not peace, so he does not mark. So this is a required example.

In this problem, we have been asked to state and give examples for modest opponents and modest talents. So first of all, we have Morris opponents. All right now, modi's proponents is a form of an argument and we have two premises and a conclusion basically it is if P then Q. And then we have another promise pete. And then using modus opponents, we can conclude that we have Q. So if we want to give an example, we can consider if today is sunday. Yeah, then I will go to the store, then another premises. Today is sunday. So you have if P then Q. And then we have peace. So according to Mona's opponents, the conclusion will be cute. So the conclusion will be I will go to the store next. We need to consider Morris Collins. Now, over here, the form of the argument is 50, then Q. Not cute. Then the conclusion is not pink. So for this we can consider if today is sunday, then I will go to the store next we have not Q. So I do not go to the store. That's according to Maurice tollins, we'll have not P. So that means the conclusion will be today is not sunday. So this is a required example


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