2021 Medium
Multiple Choice
Marks: 4.00 / −2.00
Which of the following are equivalence relations? Select all that apply.
- A. Equality (=) on \( \mathbb{R} \)
- B. "is greater than" on \( \mathbb{R} \)
- C. "has the same absolute value" on \( \mathbb{R} \)
- D. "is a subset of" on a power set
Correct Options:
- A. Equality (=) on \( \mathbb{R} \) ✓ Correct
- B. "is greater than" on \( \mathbb{R} \)
- C. "has the same absolute value" on \( \mathbb{R} \) ✓ Correct
- D. "is a subset of" on a power set
Hint: Check: reflexive, symmetric, and transitive.
Solution:
Equality (=) and "same absolute value" both satisfy all three properties of an equivalence relation.
relations
equivalence