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If S equals straight lines in the plane and ab if a and b are parallel Verify that the relation is an equivalence relation on the set S given?
Establishing equivalence depends on the definition of parallel lines. If they are defined as lines which cannot ever meet (have no point in common), then the relation is not reflexive and so cannot be an equivalence relation.
However, if the lines are in a coordinate plane and parallel lines are defined as those which have the same gradient then:
- the gradient of a is the gradient of a so the relationship is reflexive ie a ~ a.
- if the gradient of a is m then b is parallel to a if gradient of b = m and, if the gradient of b is m then b is parallel to a. Thus the relation ship is symmetric ie a ~ b <=> b ~ a.
- If the gradient of a is m then b is parallel to a if and only if gradient of b = gradient of a, which is m. Also c is parallel to b if and only if gradient of c = gradient of b which is m. Therefore c is parallel to a. Thus the relation is transitive, that is a ~ b and b ~ c => a ~ c.
The relation is reflexive, symmetric and transitive and therefore it is an equivalence relationship.
What else can I help you with?
Verify that the straight line joining mid -point of any two sides of triangle is parallel to the third side and equal to half of it?
Input straight line joining mid -point of any two sides of triangle is parallel to the 3rd side and equal to half of it.
When constructing parallel lines how can you be sure the lines you constructed are parallel?
To ensure the lines you constructed are parallel, you can use a ruler or straightedge to measure the distance between the lines at multiple points; if the distance remains consistent, the lines are parallel. Alternatively, you can use a protractor to verify that corresponding angles formed by a transversal intersecting the lines are equal. Lastly, using a compass to create equal distances from a reference point to both lines can also confirm their parallelism.
What is the noun form of the verb verify?
The noun forms of the verb to verify are verifier, verification, and the gerund, verifying.
Which transformation can verify congruence by sliding one triangle over another apex?
The transformation that can verify congruence by sliding one triangle over another is called a translation. During this transformation, one triangle is moved (or "slid") along a straight path without rotating or flipping it, allowing for direct comparison of corresponding sides and angles. If the triangles align perfectly after the translation, it confirms that they are congruent.
How do you use the word verification in a sentence?
Verify- airport officials need to verify passports to see if it's them or not.
Verify that the straight line joining mid -point of any two sides of triangle is parallel to the third side and equal to half of it?
Input straight line joining mid -point of any two sides of triangle is parallel to the 3rd side and equal to half of it.
How far Ohm's Law is verified for series and parallel circuit?
You cannot 'verify' Ohm's Law with a series or parallel circuit. The only way of verifying Ohm's Law is to plot a graph of current against voltage for variations in voltage. If the resulting graph is a straight line, then you have verified Ohm's Law for the load you have used.
Ranger wants to verify that the expression8x – 20 is the correct simplified expression for 4(2x – 5). Explain how to verify the simplified expression?
Sample Answer: To verify, a number needs to be substituted for x in both expressions. Use order of operations to simplify and find the value. The value needs to be the same for both expressions to prove equivalence.
Is it possible that there are parallel universes which form the multiverse?
It is entirely possible, but difficult to verify, one way or the other.
How will you Verify that the set of all straight lines under the relationparallel to is an equivalence relation?
Suppose S is a set of all lines.Then for any line s in S, s s (reflexive);For any two lines s and t in S, s t if and only if t s (symmetric);For any three line, s, t and u in S, s t and t u => s u.Each of these statements are easy to prove if you use the slope-intercept or standard form of the lines' equations.
What is the best way to wire your subs to get the most power?
You get more power by wiring the speakers in parallel, but you need to verify that the amplifier can handle that configuration or you may blow the amp.
How can you verify the verticality of an object using a piece of string with a weight on the end?
For this hammer a nail very close to the object into the object and hang the string on that nail. Then let the string with weight stop swinging (best to do it in an enclosed room with no wind). When the string stops swinging, if the straight-edged object is parallel with the string, then the object is completely vertical
When constructing parallel lines how can you be sure the lines you constructed are parallel?
To ensure the lines you constructed are parallel, you can use a ruler or straightedge to measure the distance between the lines at multiple points; if the distance remains consistent, the lines are parallel. Alternatively, you can use a protractor to verify that corresponding angles formed by a transversal intersecting the lines are equal. Lastly, using a compass to create equal distances from a reference point to both lines can also confirm their parallelism.
The total resistance of a circuit with three 30 ohm resistors in parallel is ohms?
If the parallel resistors are equal, then the total resistance (in this case, with three resistors) will decrease by a factor of 3. I suggest you verify this with the standard formula for parallel resistance: 1/R = 1/R1 + 1/R2 + 1/R3, replacing the value 30 for R1, R2, and R3, and calculating R, the combined resistance.
A sentence for verify?
Can you verify your identity.
Sentence for verify?
Can you verify your identity.
What is the opposite of verify?
Opposite of 'verify' = disprove.
