Question

question 14 (1 point)
find the cardinal number of each set.

\\{5, 10, 15, 20, ...50\\}

type only the number below.

question 15 (1 point)
select the contrapositive of the following statement.

if my coffee is cold then i will heat it up.

• if i will heat it up then my coffee is cold.
• if my coffee is cold then i will heat it up.
• if i will not heat it up then my coffee is not cold.
• if my coffee is not cold then i will not heat it up.

Explanation:

🆕 New Concept Discovered: Cardinality and Contrapositive
Counting elements and negating conditional statements.

Step 1: Solve Question 14 (Cardinal Number)

The cardinal number of a set is the number of elements in that set.

The given set is:

$$ \{5, 10, 15, 20, \dots, 50\} $$

This is an arithmetic progression where each term is a multiple of \(5\). We can express the elements as:

$$ 5 \times n $$

where \(n\) ranges from \(1\) to some maximum integer.

To find the number of terms, divide the last term by the common difference:

$$ n = \frac{50}{5} = 10 $$

The set contains exactly \(10\) elements.

Step 2: Solve Question 15 (Contrapositive Statement)

A conditional statement has the form:

$$ \text{If } P \text{ then } Q $$

Its contrapositive is formed by swapping and negating both parts:

$$ \text{If not } Q \text{ then not } P $$

For the given statement:

• \(P\): "my coffee is cold"
• \(Q\): "I will heat it up"

Applying the contrapositive rule:

• "not \(Q\)": "I will not heat it up"
• "not \(P\)": "my coffee is not cold"

Putting it together:
"If I will not heat it up then my coffee is not cold."

This matches the third option.

Answer:

Question 14:
10

Question 15:
If I will not heat it up then my coffee is not cold.