Multiple Choice Questions
Discrete Mathematics: Logic and Sets
Topic: Discrete Mathematics: Logic and Sets
Grade: 10
Question 1:
Which of the following statements is equivalent to the statement \”If it is raining, then the ground is wet\”?
a) It is raining and the ground is wet.
b) If the ground is wet, then it is raining.
c) If it is not raining, then the ground is not wet.
d) If the ground is wet, then it is not raining.
Answer: b) If the ground is wet, then it is raining.
Explanation: The original statement can be rewritten as \”If A, then B\”. The equivalent statement would be \”If B, then A\”. In this case, A represents \”it is raining\” and B represents \”the ground is wet\”. So, if the ground is wet, it implies that it is raining. For example, if the sprinklers are on and the ground is wet, it means it is raining.
Question 2:
Which of the following statements is false?
a) If x is an even number, then x + 2 is also even.
b) If x is an odd number, then x + 1 is also odd.
c) If x is an even number, then x – 1 is also even.
d) If x is an odd number, then x – 2 is also odd.
Answer: d) If x is an odd number, then x – 2 is also odd.
Explanation: This statement is false because if we take an odd number, let\’s say 5, and subtract 2 from it, we get 3 which is an odd number. This contradicts the statement. However, the other statements are true. For example, if we take an even number like 4, adding 2 to it gives us 6 which is also even.
Question 3:
Which of the following is the contrapositive of the statement \”If it is sunny, then I will go to the beach\”?
a) If it is not sunny, then I will not go to the beach.
b) If I will not go to the beach, then it is not sunny.
c) If I will go to the beach, then it is sunny.
d) If it is not sunny, then I will go to the beach.
Answer: a) If it is not sunny, then I will not go to the beach.
Explanation: The contrapositive of a conditional statement switches the hypothesis and the conclusion, and negates both. In this case, the original statement is \”If A, then B\”. The contrapositive would be \”If not B, then not A\”. So, if it is not sunny, it implies that I will not go to the beach. For example, if it is raining, it is not sunny, and I will not go to the beach.
Question 4:
Which of the following sets represents the union of sets A = {1, 2, 3} and B = {3, 4, 5}?
a) {1, 2, 3, 4, 5}
b) {1, 2, 3}
c) {3}
d) {4, 5}
Answer: a) {1, 2, 3, 4, 5}
Explanation: The union of two sets includes all elements that are in either set. In this case, the union of sets A and B would be {1, 2, 3, 4, 5}. For example, if set A represents the set of even numbers and set B represents the set of odd numbers, their union would include all numbers.
Question 5:
Which of the following sets represents the intersection of sets A = {1, 2, 3} and B = {3, 4, 5}?
a) {1, 2, 3, 4, 5}
b) {1, 2, 3}
c) {3}
d) {4, 5}
Answer: c) {3}
Explanation: The intersection of two sets includes all elements that are common to both sets. In this case, the intersection of sets A and B would be {3}. For example, if set A represents the set of prime numbers and set B represents the set of odd numbers, their intersection would include the number 3.
Note: This is the first part of the response. The remaining questions and explanations will be provided in subsequent responses due to space limitations.