Mathematics

Problem

Let

A = \{x \in \mathbb Z \mid -3 \le x \le 3\}

and define a relation

R

A

R = \{(x,y) \in A \times A \mid y = x^{2} - 2x\}

. Consider the ordered pair

(t-1,\,t^{2} - 3t + 2)

. For which value of

t

given below is this pair a member of

R

? a)

-1

2

1

3

Intuitive explanation

The key is recognizing that for an ordered pair to belong to $R$ , it must satisfy the defining rule $y = x^2 - 2x$ . So you need to match the first coordinate with $x$ and the second with $y$ , then check whether the equation holds. This becomes a problem of solving for $t$ such that $t^2 - 3t + 2 = (t-1)^2 - 2(t-1)$ —essentially substituting the given expressions into the relation's formula and simplifying to find which value of $t$ makes it true.

Intuitive explanation

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