Final answer:
It is false that all even numbers (except for 2) are composite numbers; some even prime numbers only have two factors. Basic probability terms, set theory, and the commutative property of addition are explained. Also, waves with different frequencies can indeed superimpose.
Step-by-step explanation:
It is false that all even numbers (except for 2) are composite numbers. This statement overlooks the fact that the definition of a composite number is a number that has more than two factors; hence, any even prime number, namely 2, does not satisfy this definition as it only has two factors, 1 and itself.
In regard to the list given:
- Event T = the outcome is two. This statement's truth depends on the context of the experiment or game being referred to.
- Event A = the outcome is an even number. Based on the given sample space S, event A contains the even numbers from 1 to 19.
- Event B = the outcome is less than four. This would include the numbers 1, 2, and 3.
- The complement of A involves all the outcomes in the sample space that are not even numbers.
- A GIVEN B refers to the probability of A happening given that B has occurred.
- B GIVEN A refers to the probability of B happening given that A has occurred.
The addition property A+B=B+ A expresses the commutative property of addition, which holds true for ordinary numbers.
In the context of set theory, the sample space S is the set of whole numbers from 1 to 19. Event A (the even numbers within the sample space) would include 2, 4, 6, 8, 10, 12, 14, 16, and 18. Event B (numbers greater than 13) includes 14, 15, 16, 17, 18, and 19. The intersection of A AND B contains the numbers that are both even and greater than 13, which can be found by finding the common elements in both sets.
The statement about wave superposition, Waves can superimpose if their frequencies are different, is true. Superposition of waves with different frequencies leads to various phenomena such as beats and interference patterns.