Question

Which statement is true?

1-31 = 3 and -1-4| = -4
1-31 = 3 and 1-4| = -4
-131 = 3 and 14| = 4
1-31 = 3 and -14| = 4

Answer 1

|-3| = 3 and -|-4| = -4

Explanation:

The absolute value function changes the sign to positive, if it isn't already. The usual rules of arithmetic and logic apply to these statements.

|-3| = 3 (true) and -|-4| = -4 (true) ⇒ this statement is true

|-3| = 3 (true) and |-4| = -4 (false) ⇒ this statement is false

-|3| = 3 (false) and |4| = 4 (true) ⇒ this statement is false

|-3| = 3 (true) and -|4| = 4 (false) ⇒ this statement is false

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Additional comment

A compound "and" statement is only true if all of the parts of it are true.