2.1 Statements and Quantifiers

Determine whether each of the following sentences represents a logical statement. If it is a logical statement, determine whether it is true or false.

1. Tiger Woods won the Master’s golf championship at least five times.
2. Please, sit down over there.
3. All cats dislike dogs.

Write each of the following logical statements in symbolic form.

1. Barry Bonds holds the Major League Baseball record for total career home runs.
2. Some mammals live in the ocean.
3. Ruth Bader Ginsburg served on the U.S. Supreme Court from 1993 to 2020.

Write the negation of each logical statement in words.

1. Michael Phelps was an Olympic swimmer.
2. Tom is a cat.
3. Jerry is not a mouse.

Write the negation of each logical statement symbolically.

1. $p$: Michael Phelps was an Olympic swimmer.
2. $r$: Tom is not a cat.
3. $\sim q$: Jerry is not a mouse.

Given the statements:

$r$: Elmo is a red Muppet.

$p$: Ketchup is not a vegetable.

1. Write the symbolic form of the statement, “Elmo is not a red Muppet.”
2. Translate the statement $\sim p$ into words.

For each series of premises, draw a logical conclusion to the argument that includes one of the following quantifiers: all, some, or none.

1. Squares and rectangles have four sides. A square is a parallelogram, and a rectangle is a parallelogram. What conclusion can be drawn from these premises?
2. $1 + 2 = 3 ,$ $6 + 7 = 13 ,$ and $23 + 24 = 47.$ Of these, 1 and 2, 6 and 7, and 23 and 24 are consecutive integers; 3, 13, and 47 are odd numbe…

Given the statements:

$p$: All leopards have spots.
$r$: Some apples are red.
$s$: No lemons are sweet.

Write each of the following symbolic statements in words.

1. $\sim p$
2. ~$r$
3. $\sim s$