State which of the following are logical statements and then classify the statements as true or false.
a) 1 + 4 = 6
b) She is in our class
c) Butte is the capital of Montana
d) 3 + x = x + 3
a) illogical nonidentity because 4 does not equal 5
b) testable statement. i don't know your definition of logical statement and can't be of much more help here
3) false obviously
d) logical statement due to commutative prop of addition
To determine if a statement is a logical statement, we need to assess whether it is capable of being either true or false.
Now, let's evaluate each statement:
a) "1 + 4 = 6": This statement is false because the sum of 1 and 4 is equal to 5, not 6. Therefore, it is a logical statement that is false.
b) "She is in our class": Without more information, it is impossible to determine the truth value of this statement. We need to know who "she" refers to and what "our class" refers to. As it stands, this statement is not a logical statement since it cannot be classified as either true or false.
c) "Butte is the capital of Montana": This statement is false. The capital of Montana is Helena, not Butte. Therefore, it is a logical statement that is false.
d) "3 + x = x + 3": This statement is a mathematical equation. It is true regardless of the value of "x". In other words, it is a logical statement that is true for all values of "x".
To summarize:
a) Logical statement: False
b) Not a logical statement
c) Logical statement: False
d) Logical statement: True