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Question
Write the component statement of the compound statement and check whether the compound statement is true or false:
x = 2 and x = 3 are the roots or the equation 3x2 − x − 10 = 0.
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Solution
The component statements of the given compound statement are:
1) \[x = 2\] is the root or the equation \[3 x^2 - x - 10 = 0\]
2) \[x = 3\] is the root or the equation \[3 x^2 - x - 10 = 0\]
The connective used is "and". So, both component statements must be true for the compound statement to be true. The statement " \[x = 3\] is the root or the equation \[3 x^2 - x - 10 = 0\] " is false. Therefore, the compound statement is false.
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