“If Mary and Tom are classmates, then they go to the same school.”
Which statement below is logically equivalent?
If Mary and Tom do not go to the same school, then they are not classmates.
If Mary and Tom are not classmates, then they do not go to the same school.
If Mary and Tom go to the same school, then they are classmates.
If Mary and Tom go to the same school, then they are not classmates.
The statement "If Mary and Tom are classmates, then they go to the same school" can be rephrased using logical equivalences to determine which of the given statements is logically equivalent. Let's go through each option:
1. "If Mary and Tom do not go to the same school, then they are not classmates": This statement is not logically equivalent to the original statement. It assumes the converse of the original statement, which may not hold true. For example, Mary and Tom may not go to the same school, but they can still be classmates if they take a particular class together outside of school.
2. "If Mary and Tom are not classmates, then they do not go to the same school": This statement is logically equivalent to the original statement. It is the contrapositive, which maintains the logical relationship.
3. "If Mary and Tom go to the same school, then they are classmates": This statement is not logically equivalent to the original statement. It assumes the converse of the original statement, which may not hold true. For example, Mary and Tom may go to the same school but not know each other or be in different grades, so they are not necessarily classmates.
4. "If Mary and Tom go to the same school, then they are not classmates": This statement is not logically equivalent to the original statement. It is the inverse of the original statement, which has a different logical truth value.
Therefore, the correct statement that is logically equivalent to the original statement is option 2: "If Mary and Tom are not classmates, then they do not go to the same school."
..... DEEZNUTS!
#TRUMP2069