(a.)
Whether the given statement is logically equivalent to the statement “If every digit of a number is
It has been determined that the given statement is not logically equivalent to the statement “If every digit of a number is
Given:
If every digit of a number is not
Concept used:
The conditional statement “If
An implication and its contrapositive are logically equivalent. The converse and the inverse of a conditional statement are logically equivalent.
Calculation:
The reference statement is given as:
“If every digit of a number is
The given statement is:
“If every digit of a number is not
Clearly the given statement is inverse of the reference statement.
As discussed, an implication and its inverse are not logically equivalent.
Hence, the given statement is not logically equivalent to the reference statement.
Conclusion:
It has been determined that the given statement is not logically equivalent to the statement “If every digit of a number is
(b.)
Whether the given statement is logically equivalent to the statement “If every digit of a number is
It has been determined that the given statement is logically equivalent to the statement “If every digit of a number is
Given:
If a number is not divisible by
Concept used:
The conditional statement “If
An implication and its contrapositive are logically equivalent. The converse and the inverse of a conditional statement are logically equivalent.
Calculation:
The reference statement is given as:
“If every digit of a number is
The given statement is:
“If a number is not divisible by
Clearly the given statement is contrapositive of the reference statement.
As discussed, an implication and its contrapositive are logically equivalent.
Hence, the given statement is logically equivalent to the reference statement.
Conclusion:
It has been determined that the given statement is logically equivalent to the statement “If every digit of a number is
(c.)
Whether the given statement is logically equivalent to the statement “If every digit of a number is
It has been determined that the given statement is not logically equivalent to the statement “If every digit of a number is
Given:
If a number is divisible by
Concept used:
The conditional statement “If
An implication and its contrapositive are logically equivalent. The converse and the inverse of a conditional statement are logically equivalent.
Calculation:
The reference statement is given as:
“If every digit of a number is
The given statement is:
“If a number is divisible by
Clearly the given statement is converse of the reference statement.
As discussed, an implication and its converse are not logically equivalent.
Hence, the given statement is not logically equivalent to the reference statement.
Conclusion:
It has been determined that the given statement is not logically equivalent to the statement “If every digit of a number is
Chapter B.2 Solutions
PRECALCULUS:GRAPHICAL,...-NASTA ED.
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