Question

Describe the difference in the graph of the conjunction “x > 2 and x < 10” and the graph of the disjunction “x > 2 or x > 10.”

Answer 1

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Answer:

• 2 < x < 10 -- shaded between 2 and 10
• 2 < x or 10 < x -- shaded right of 2

Explanation:

x > 2 and x < 10

The expression x > 2 graphs as an open circle at x=2 and shading of the number line to the right of that.

The expression x < 10 graphs as an open circle at x=10 and shading to the left of that. The conjunction 'and' means that the only values of interest are those where the shading overlaps, between (and not including) 2 and 10.

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x > 2 or x > 10

The graph of x > 2 is described above.

The expression x > 10 graphs as an open circle at x=10 and shading to the right of that. The conjunction 'or' means that any shaded value is of interest. Since all values to the right of x=2 are shaded, that is what the graph of this conjunction looks like.