Question

# Venus has switches at the top and bottom of her stairs to control the light for the stairwell. She notices that when the upstairs switch is up and the downstairs switch is down, the light is turned on. a. Copy and complete the truth table. b. If both the upstairs and downstairs switches are in the up position, will the light be on? Explain your reasoning. c. If the upstairs switch is in the down position and the downstairs switch is in the up position, will the light be on? d. In general, how should the two switches be positioned so that the light is on?

Solution

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Step 1
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(a)

Let's complete the given truth table.

First, list all possibilities in the first two columns and then fill the last column.

Keep in the mind that light is turned on when the upstairs switch is up and the downstairs switch is down.

Therefore,

Upstairs Downstairs Light on
up up F
up down T
down up F

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