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Question
State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.
Every real number is a complex number.
Solution
It is a statement that is true. Hence, its truth value is T.
By the definition of a complex number,
If A and B are any real numbers then any number of the form A + Bi is called a complex number.
Let X be any real number. Then X can be rewritten as X + 0i, Which is in the form of A + Bi, which is a complex number.
Then every real number is a complex number with imaginary part 0.
Notes
The answer in the textbook is incorrect.
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