Question

write \\( \subset \\) or \\( \
ot\subset \\) in the blank so that the resulting statement is true. 17) \\{red, blue, green\\} \\___ \\{blue, green, yellow, black\\} a) \\( \subset \\) b) \\( \
ot\subset \\) use \\( \subseteq \\), \\( \subset \\), or both \\( \subset \\) and \\( \subseteq \\) to make a true statement. 18) \\{6,7,8\\} \\___ \\{6,7,8\\} a) \\( \subseteq \\) b) \\( \subset \\) and \\( \
ot\subset \\) c) \\( \subset \\) d) \\( \
ot\subset \\) use the formula for the cardinal number of the union of two sets to solve the problem. 19) set a contains 8 letters and 12 numbers. set b contains 12 letters and 8 numbers. two letters and 5 numbers are common to both sets a and b. find the number of elements in set a or set b. a) 33 b) 47 c) 27 d) 40

Explanation:

Step1: Analyze subset for Q17

Check if all elements of $\{\text{red, blue, green}\}$ are in $\{\text{blue, green, yellow, black}\}$. The element "red" is not in the second set, so the first set is not a subset.

Step2: Analyze set relation for Q18

Check if $\{6,7,8\}$ is a subset/proper subset of itself. A set is always a subset of itself ($\subseteq$), but not a proper subset ($\subset$) since they are equal.

Step3: Calculate total elements in Set A

Set A has $8 + 12 = 20$ total elements.

Step4: Calculate total elements in Set B

Set B has $12 + 8 = 20$ total elements.

Step5: Calculate common elements total

Common elements: $2 + 5 = 7$ elements.

Step6: Apply union formula

Use $n(A \cup B) = n(A) + n(B) - n(A \cap B)$
$\displaystyle n(A \cup B) = 20 + 20 - 7 = 33$

Answer:

1. B) $

subseteq$

1. A) $\subseteq$
2. A) 33