Identify the digit in the first decimal place, which is 0.

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Here are the solutions to the problems:

1. (a) Express 6.093 to one decimal place.

Identify the digit in the first decimal place, which is 0.
Look at the digit immediately to its right, which is 9.
Since $9 \ge 5$ , round up the digit in the first decimal place.
$6.093 \approx \boxed{6.1}$
1. (b) Evaluate $\frac{3}{4} + \frac{1}{2} - \frac{1}{3}$ .
Find a common denominator for $4, 2,$ and 3.
The least common multiple (LCM) is 12.
Convert each fraction to have a denominator of 12.
$\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}$ $\frac{1}{2} = \frac{1 \times 6}{2 \times 6} = \frac{6}{12}$ $\frac{1}{3} = \frac{1 \times 4}{3 \times 4} = \frac{4}{12}$
Perform the addition and subtraction.
$\frac{9}{12} + \frac{6}{12} - \frac{4}{12} = \frac{9 + 6 - 4}{12} = \frac{15 - 4}{12} = \boxed{\frac{11}{12}}$
2. Given the sets $A = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}$ and $B = \{2, 3, 6, 7\}$ .

2. (a) Find $A'$ .
Assuming that $A$ is the universal set for this context, the complement of $A$ ( $A'$ ) would be the set of elements in the universal set that are not in $A$ .
$A' = A \setminus A = \boxed{\emptyset}$
2. (b) Find $A \cap B$ .
$A \cap B$ represents the intersection of sets $A$ and $B$ , which includes all elements common to both sets.
$A = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}$ $B = \{2, 3, 6, 7\}$
The elements common to both sets are $2, 3, 6, 7$ .
$A \cap B = \boxed{\{2, 3, 6, 7\}}$
2. (c) Find $n(B)$ .
$n(B)$ represents the number of elements in set $B$ .
$B = \{2, 3, 6, 7\}$
There are 4 elements in set $B$ .
$n(B) = \boxed{4}$
3. Complete the truth table below.
Fill the $\sim P$ column by negating the truth values of $P$ .
Fill the $\sim P \lor Q$ column by applying the OR operator to the values in the $\sim P$ column and the $Q$ column.
The OR operator is true if at least one of its operands is true.

P Q $\sim P$ $\sim P \lor Q$
T T F T
T F F F
F T T T
F F T T

Identify the digit in the first decimal place, which is 0.

Step-by-step solution

Identify the digit in the first decimal place, which is 0.

Look at the digit immediately to its right, which is 9.

Since $9 \ge 5$ , round up the digit in the first decimal place.

Find a common denominator for $4, 2,$ and 3.

Convert each fraction to have a denominator of 12.

Perform the addition and subtraction.

Fill the $\sim P$ column by negating the truth values of $P$ .

Fill the $\sim P \lor Q$ column by applying the OR operator to the values in the $\sim P$ column and the $Q$ column.

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More Mathematics Questions

Identify the digit in the first decimal place, which is 0.

Step-by-step solution

Identify the digit in the first decimal place, which is 0.

Look at the digit immediately to its right, which is 9.

Since 9≥59 \ge 59≥5, round up the digit in the first decimal place.

Find a common denominator for $4, 2,$ and 3.

Convert each fraction to have a denominator of 12.

Perform the addition and subtraction.

Fill the ∼P\sim P∼P column by negating the truth values of PPP.

Fill the ∼P∨Q\sim P \lor Q∼P∨Q column by applying the OR operator to the values in the ∼P\sim P∼P column and the QQQ column.

Still stuck on this one?

More Mathematics Questions

Since $9 \ge 5$ , round up the digit in the first decimal place.

Fill the $\sim P$ column by negating the truth values of $P$ .

Fill the $\sim P \lor Q$ column by applying the OR operator to the values in the $\sim P$ column and the $Q$ column.