Use the set notation symbol ‘is an element of’ (∈).

Use the Venn diagram to determine which statement correctly describes the relationship between the sets $P$, $Q$, and the elements shown.

Consider the sets $A = \{x \in \mathbb{R} : x^2 - 7x + 10 = 0\}$ and $B = \{1, 2, 3, 4, 5, 6\}$. (a) Determine the elements of set $A$ by solving the equation. Express your answer using set notation. (1 mark) (b) Use the symbol $\in$ to write a statement showing whether the value $5$ belongs to set $A$. (1 mark) (c) If $n \in A$ and $n$ is also the larger element in $A$, calculate the value of $n^2 - 10$. (1 mark)

Consider the function $f(x) = x^2 - 5x + 6$ with domain $D = \{x \in \mathbb{R} : 0 \leq x \leq 5\}$ and range $R$. a) Determine the range $R$ of the function. Express your answer using set notation with appropriate inequalities. (2 marks) b) Use the result from part a) to verify whether $-0.25 \in R$ by showing your reasoning. (1 mark)

Consider the sets defined in the stimulus. Determine whether each of the following statements is true or false, providing justification using set notation: (a) $-4 \in A$ (b) $4 \in B$ (c) $6 \in C$ (d) $2i \in E$

Consider the five sets A, B, C, D and E defined in the table above. (a) Determine whether −3 ∈ A is true or false. Justify your answer by checking the membership conditions. (b) Determine whether 4 ∈ B is true or false. Justify your answer by checking the membership conditions. (c) Determine whether √2 ∈ D is true or false. Justify your answer by checking the membership conditions. (d) Determine whether 2i ∈ E is true or false. Justify your answer by checking the membership conditions.

Use the set notation symbol ∈ to complete the statement: Given $A = \{x \in \mathbb{Z} : -3 < x \leq 5\}$, which of the following is true?