Assume that the universal set is Z. Consider the following sentence: (3t = Z) (t •x = 20). (a) Explain why this sentence is an open sentence and not a statement. (b) If 5 is substituted for x, is the resulting sentence a statement? If it is a statement, is the statement true or false? (c) If 8 is substituted for x, is the resulting sentence a statement? If it is a statement, is the statement true or false? (d) If -2 is substituted for x, is the resulting sentence a statement? If it is a statement, is the statement true or false?

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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6. Assume that the universal set is Z. Consider the following sentence:
(t ≤ Z) (t • x = 20).
(a) Explain why this sentence is an open sentence and not a statement.
(b) If 5 is substituted for x, is the resulting sentence a statement? If it is a
statement, is the statement true or false?
(c) If 8 is substituted for x, is the resulting sentence a statement? If it is a
statement, is the statement true or false?
(d) If -2 is substituted for x, is the resulting sentence a statement? If it is
a statement, is the statement true or false?
Transcribed Image Text:6. Assume that the universal set is Z. Consider the following sentence: (t ≤ Z) (t • x = 20). (a) Explain why this sentence is an open sentence and not a statement. (b) If 5 is substituted for x, is the resulting sentence a statement? If it is a statement, is the statement true or false? (c) If 8 is substituted for x, is the resulting sentence a statement? If it is a statement, is the statement true or false? (d) If -2 is substituted for x, is the resulting sentence a statement? If it is a statement, is the statement true or false?
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