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Chapter 1: Q4E (page 12)

What is the negation of each of these propositions?

a) Jennifer and Teja are friends.

b) There are 13items in a baker’s dozen.

c) Abby sent more than100text messages every day.

d) 121is a perfect square.

Short Answer

Expert verified
  1. Jennifer and Teja are not friends.
  2. There are either more than 13 or less than 13 items in a baker’s dozen.
  3. Abby sent less than or equal to 100text messages every day.
  4. 121is not a perfect square.

Step by step solution

01

Definition of negation

The negation of a statement is the opposite of the given statement.

02

Negation of statement in a)

Jennifer and Teja are not friends.

03

Negation of statement in b)

There are either more than 13or less than13 items in a baker’s dozen.

04

Negation of statement in c)

Abby sent less than or equal to 100text messages every day.

05

Negation of statement in d)

121is not a perfect square.

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Most popular questions from this chapter

Each inhabitant of a remote village always tells the truth or always lies. A villager will give only a “Yes” or a “No” response to a question a tourist asks. Suppose you are a tourist visiting this area and come to a fork in the road. One branch leads to the ruins you want to visit; the other branch leads deep into the jungle. A villager is standing at the fork in the road. What one question can you ask the villager to determine which branch to take?

Show that¬and∧form a functionally complete collection of logical operators.

What is the value of x after each of these statements is encountered in a computer program, if x = 1 before the statement is reached?

a) if x+2=3then x=x+1
b) if (x+1=3)OR (2x+2=3)then x=x+1
c) if (2x+3=5)AND (3x+4=7)then x=x+1
d) if (x+1=2)XOR (x+2=3)then x=x+1
e) if x < 2 thenx=x+1

Let p and q be the propositions p : It is below freezing. q : It is snowing. Write these propositions using p and q and logical connectives (including negations).

a) It is below freezing and snowing.
b) It is below freezing but not snowing.
c) It is not below freezing and it is not snowing.
d) It is either snowing or below freezing (or both).
e) If it is below freezing, it is also snowing.
f )Either it is below freezing or it is snowing, but it is not snowing if it is below freezing.
g) That it is below freezing is necessary and sufficient for it to be snowing.

Let Q(x,y)be the statement “xhas sent an e-mail message to y,” where the domain for both xand yconsists of all students in your class. Express each of these quantifications in English.

(a) ∃x∃yQ(x,y) (b) ∃x∀yQ(x,y)

(c)∀x∃yQ(x,y) (d)∃y∀xQ(x,y)

(e)∀y∃xQ(x,y) (f)∀x∀yQ(x,y)
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