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Consider the unary relational symbols P and L, and the binary relational symbol On, where P(a) and I(a) encode that a is a point and a (straight) line in the 2-dimensional space, respectively, while On(a,b) encodes that a is a point, b is a line, and o lies on b.
Write first-order formulas over these relational symbols expressing the following (you can use the equality relation between lines/points):
(a) On every line, there lie at least two different points.
(b) Any two lines sharing at least two different points are identical.
(c) For any two different points, there exists exactly one line on which they lie.
The functions {sinmx; cosmx}; m = 0,....∞ form a complete set over the interval x ∈ [ -Π, Π]. That is, any function f(x) can be expressed as a linear superposition of these
Find the equation for each of the two planes that just touch the sphere (x - 1) 2 + (y - 4) 2 + (z - 2)2 = 36 and are parallel to the yz-plane. And give the points on the sphere
#stioquen..Store A is advertising a sale that will reduce prices on all merchandise by 15%. Store B is advertising a sale that will reduce prices on all merchandise by one over fiv
If the p th term of an AP is q and the q th term is p. P.T its n th term is (p+q-n). Ans: APQ a p = q a q = p a n = ? a + (p-1) d = q a + (q-1) d = p
find the volume of a rectangular based right pyramid with its base 18 cm by 24 cm and the slanted edge 39 cm
There are 81 women teachers at Russell High. If 45% of the teachers in the school are women, how many teachers are there at Russell High? Use the proportion part/whole = %/100.
poa is a straight line in circle,wher o is center of circle,b is any pointjoined with p.prove that pa>pb
2/2
If the areas of three adjacent faces of cuboid are x, y, z respectively, Find the volume of the cuboids. Ans: lb = x , bh = y, hl = z Volume of cuboid = lbh V 2 = l 2 b 2
(x+y+1)dy/dx=1
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