The following are hypothetical exchange rates: 2 euros = 1 pound; $1 = 2 pounds. We can conclude that

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To determine the relationship between the euro and the dollar, we need to convert the exchange rates given in the question.

Given:
1 pound = 2 euros
1 dollar = 2 pounds

To convert euros to dollars, we need to multiply the two exchange rates:

1 euro = 1/2 pound (since 2 euros = 1 pound)
1 euro = 1/2 * 2 dollars (substituting the value of 1 pound in dollars)
1 euro = 1 dollar

Therefore, we can conclude that 1 euro is equivalent to 1 dollar.