Savannah State University Department of Mathematics MATH 2301 Exercises I Fall 2

Question

Savannah State University Department of Mathematics MATH 2301 Exercises I Fall 2017 Introduction to Discrete Mathematics 1) write the following statements using-o" and find the negation, the converse, inverse and contrapositive :1 hor A"1 a@thesnowisgooaoherl willgoskiing.esnoo b) x is a natural number only if x is an integer : then I will op skiina P: converse on Dack> c) x is a natural number whenever x is an integer Determine if it is a tautology or a contradiction or neither. II) II) Determine which of the following statements are tautologies using the quick method where Possible. IV) Using logically equivalent statements, without the direct use of truth tables, to show a)-(-pAqA ( pv q) = p V) Translate into symbols the following compound statements and give the form of the compound statement. In each case, list the statements p, r P x Is odd odd (a) If x is odd and y is odd then x +y is even. Q:y (b) It is not both raining and hot. (c) It is neither raining nor hot. (d) It is raining but it is hot. (e)-1xs2 is of Equivalence, write the following logical expressions vIl) Using Logical Equivalences and Substitution using V and A only (even without) b) (y SO)-(01) .

Explanation / Answer

(According to Chegg policy, if questions have multiple subquestions, only the first one with all subquestions will be solved. Please post the remaining in another question)

1. a. Let p: Snow is good and q: I will go skiing

The statement is "If the snow is good then I will go skiing"

This can be written as p => q

Converse is q => p : "If I will go skiing, then the snow is good"

Inverse is ~p => ~q: "If the snow is not good, then I will not go skiing"

Contrapositive is ~q => ~p: "If I will not go skiing, then the snow is not good"

Negation is ~(p => q)

By rule of material implication, this is ~(~p v q) and by De-Morgan's law this is p ^ ~q

In words, "The snow is good and I will not go skiing".

b. Let p: x is a natural number and q: x is an integer

Given statement is p => q

Converse is q => p: If x is an integer then x is a natural number

Inverse is ~p => ~q: If x is not a natural number then x is not an integer

Contrapositive is ~q => ~p: If x is not an integer then x is not a natural number

Negation (as per the earlier example) is p ^ ~q: x is a natural number and x is not an integer

c. Let p: x is a natural number and q: x is an integer

The given statement is q => p

Converse is p => q: If x is a natural number then x is an integer

Inverse is ~q => ~p: If x is not an integer then x is not a natural number

Contrapositive is ~p => ~q: If x is not a natural number then x is not an integer

Negation (as per the earlier example) is q ^ ~p: x is an integer and x is not a natural number

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

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