Question

Notify Me Bookmark

Consider the relation R = (x, y) ∈ R × R : x - y ∈ Z on R. Prove that relation R is reflexive and symmetric, and transitive.

Consider the relation R = (x, y) ∈ R × R : x - y ∈ Z on R. Prove that relation R is reflexive and symmetric, and transitive.

Image text
Consider the relation R = {(x, y) E R
Consider the relation R = ( x , y ) ∈ R × R : x − y ∈ Z on R . Prove that relation R is refexive and symmetric, and transitive.

Detailed Answer

1 0

Please enter your email here. You will get email when this question is answered by our tutor.

Answer
Doubtrix Logo

This Problem has been solved!

You'll get a detailed, step-by-step and expert verified solution.

Join Doubtrix with 7-days free trial

  • Icon Correct & Verified Answers
  • Icon No AI-Generated Answers
  • Icon Video Solution for Difficult Questions
  • Icon Work With Experts to Reach at Correct Answers
Login Sign Up
  • Student Reviews:
  • (1)
  • Correct answers (1)
  • Complete solution (1)
  • Step-by-step solution (1)
  • Fully explained (1)

Similar/Related Questions

Consider the relation R = (x, y) = R x R : |x

Solution
1 0

(a) For the relation {(6,6), (6,7), (6,8), (7,6), (7,7), (7,8)} on the set {5,6,7,8}, decide whether it is reflexive, symmetric and transitive or not. (b) For relation R = {(a,b): a,b E A, |a

Solution
1 0

Consider the current mirror circuit shown in Figure 4 on page 6 where an additional resistor R is connected between the gates of the MOSFETS and ground. Assume all transistors are in saturation and you can ignore Early effect. (a) Given that IREF = 250 µA, Kn’ for the MOSFET is 10 µA/V2, VTN = 1 V, (W/L)1 = 5, (W/L)2 = 10 and R = 20 kΩ, find the values of the DC voltage VGS1 and DC currents ID1 and ID2. (10 Marks) (b) Perform an AC small-signal analysis to find an algebraic expression of the input resistance Rin in terms of the transconductance gm of the MOSFETS and the resistor R. Indicate clearly the gm of the i-th transistor as gmi. For example, the gm of transistor M1 should be written as gm1. (5 Marks) (c) Using the transistor parameters and resistor values given in part (a), find out the magnitude of the input resistance Rin found in part (b). (5 Marks)

Consider the current mirror circuit shown in Figure 4 on page 6 where an additional resistor R is connected between the gates of the MOSFETS and ground. Assume all transistors are in saturation and you can ignore Early effect. (a) Given that IREF = 250 µA, Kn’ for the MOSFET is 10 µA/V2, VTN = 1 V, (W/L)1 = 5, (W/L)2 = 10 and R = 20 kΩ, find the values of the DC voltage VGS1 and DC currents ID1 and ID2. (10 Marks) (b) Perform an AC small-signal analysis to find an algebraic expression of the input resistance Rin in terms of the transconductance gm of the MOSFETS and the resistor R. Indicate clearly the gm of the i-th transistor as gmi. For example, the gm of transistor M1 should be written as gm1. (5 Marks) (c) Using the transistor parameters and resistor values given in part (a), find out the magnitude of the input resistance Rin found in part (b). (5 Marks)
Solution
0 0