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Determine the truth-values of the following compound propositions, using your knowledge of mathematics and logic. Assume that x represents any real number and f any function.
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- We now need to attempt to find an exact value for n such that P(r ≥ 1) = 0.99. Clearly, if the bank has any chance of detecting a burglar they will need to have at least one alarm installed. So, we know that, minimally, n must be at least 1.Since n must be at least 1, suppose we start by trying n = 2, where there will be two alarms. When there are two alarms, r ≥ 1 means either one or both alarms could detect the burglar. If neither alarm detects the burglar it is considered a failure. Therefore, P(r ≥ 1) can be calculated using either of the following formulas. P(r ≥ 1) = P(1) + P(2) P(r ≥ 1) = 1 − P ( ___ ) fill in the blankSuppose: n ≥ 3 and x,y ∈ Rn , |x - y| = d > 0 and r is some +R, Need to show: 2r = d, there is exact one z in where, |z - x| = |z - y| = rSuppose x, n ∈ N and n not equal to 0. Then, show that xnis positive if and only if x is positive.
- For #31 b) please show that for any x, y in Z(G), x(y)^-1 is also in Z(G).If f and g are in E(0, ∞), then L[ f g] = L[ f ]∗ L[g] I need help showing that this statement is false. Please, do not provide the answer involving just the Convolution Theorem, since that alone doesn't prove this statement false.Find all the values of x in the interval [0,2pi], that satisfy the question. 10cos(x)+5sin(2x)=0