) Form a conjunction from the following two statements and determine if the conjunction is true or false. Explain.
Two is an even number. Two is a prime number.
A) Two is an even number or two is a prime number.; False
B) Two is an even number and two is a prime number.; True
C) Two is an even number and two is a prime number.; False
D) Two is an even number or two is a prime number.; True
I know two is an even number, I think it is a prime number, I just don't remember why.
In logic, "or" means _either one_ of them is true. Maybe one is true, maybe the other, maybe both, but as long as at least one of the statements is true, then the whole statement is true.
Given that, cal you see which statements are true?
We define "prime number" as "divides evenly only by itself and 1" and we exclude 1 from eligibility; that explains why 2 is a prime number.
So since both are true, the statement would read "and"? So the correct answer would be B?
To answer this question, we need to understand the concepts of even numbers and prime numbers.
An even number is any integer that is divisible by 2 without leaving a remainder. In other words, if you can divide a number by 2 and get a whole number, then that number is even.
On the other hand, a prime number is a positive integer greater than 1 that has no positive integer divisors other than 1 and itself. In simpler terms, a prime number cannot be divided evenly by any other number except for 1 and itself.
Now let's examine the given statements:
1) Two is an even number. This is true because we know that any number divisible by 2 without a remainder is an even number, and since 2 divided by 2 equals 1 with no remainder, it is even.
2) Two is a prime number. This statement is also true. In order to determine whether a number is prime or not, we need to check if it has any divisors other than 1 and itself. Since 2 only has divisors 1 and 2, it meets the definition of a prime number.
Now, let's form a conjunction using the two statements and evaluate its truth value:
B) Two is an even number and two is a prime number; True
In this case, both statements are true individually, and when we combine them with the conjunction "and," the resulting conjunction is also true.
So, the correct answer is B) Two is an even number and two is a prime number, which is true.
Note: It's important to understand the definitions and properties of even and prime numbers to accurately determine the truth value of a conjunction like this.