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Determine if the relation represented by the following Boolean matrix is partially ordered.
Ans: Let the following relation R is defined on set A = {x, y, z}. To test if the relation R is partially ordered, we have to test if R is reflexive, anti symmetric and transitive.
Reflexivity: As all elements in the principal diagonal is '1', R is reflexive.
Anti Symmetry: In the following relation, we do not comprise any pairs (x, y) & (y, x) like that x ≠ y that is for (x, y) & (y, x) in R, x = y. So R is anti symmetric.
Transitivity: The relation is not transitive since for (y, x) & (x, z) in R, (y, z) is not in R. Hence R is not partially ordered.
A die is thrown repeatedly until a six comes up. What is the sample space for this experiment? HINT ;A= {6} B={1,2,3,4,5,} Ans: The sample space is = {A, BA, BBA, BBBA, BBBBA.
(a) Find an example of groups G, H, K with K H and H G but K G. (b) A subgroup H of G is characteristic if σ(H) ⊆ H for every group automorphism σ of G. Show that eve
Prove that the intercept of a tangent between two parallel tangents to a circle subtends a right angle at the centre. Since Δ ADF ≅ Δ DFC ∠ADF = ∠CDF ∴ ∠ADC = 2 ∠CDF
Given a standard 2x3 matrix show the ideal formed by the 2x2 minors is Prime.
1.)3 3/8 divided by 4 7/8 plus 3 2.)4 1/2 minus 3/4 divided by 2 3/8
A=30, B=45, b=4
SOLVE AND GRAPH THE PARABOLA NOTE: WRITE YOUR SOLUTIONS AND COMPLETE EQUATION OF GRAPH SPOINTS EACH 1. V(0,0) (0.2) P-2 2. V(0,0) E-5,0) P=-5 3. V(4-3) F(4,-2) P=1 4. V-1,5)
what is an equation for circle?..
alpha and beta are concentric angles of two points A and B on the ellipse.
sin^2alpha *sec^2beta +tan^2 beta *cos^2alpha=sin^2alpha+tan^2 beta
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