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g) Use the truth table to show that the proportion is a tautology \( [p \Lambda(p \rightarrow q] \rightarrow q \). (4mks) h) Prove that \( \forall \mu \in \mathbb{N} n^{3}-n \) is divisible by 3 . i) Given that \( f(x)=3 x^{2}+4 \) find i. \( f(2) \) ii. \( f^{-1}(7) \)
Kenya Dec 17, 2024
b) Determine whether the function F from \( \{a, b, d\} \) to \( \{1,2,3,4,5\} \) with \( f(a)=4, f(b)=5, f(c)=1 \) and \( f(d)=3 \) is one to one. c) Given that \( A=\{1,3,5\} \) and \( B=\{2,4,6\} \) find i. \( A \cap B \) ii. \( A \cup B \)
Kenya Dec 17, 2024
Exercice 1: On considère dans \( I R^{3} \), le sous ensemble \( F \) définir par: \[ F=\{(x-y, 2 x+y+4 z, 3 y+2 z) / x, y, z \in \mathbb{R}\} \] 1. Montrer que \( F \) est un sous espace vectoriel de \( I R^{3} \). 2. Donner une base de \( F \), quelle est sa dimension? 3. Fest-il égalé à \( I R^{3} \) ?
Cameroon Dec 17, 2024
Prove that the set of all rational numbers is Countable.
India Dec 17, 2024
PROBLEM SET B 1) Let \( Y=\{a, b, c, d, e\} \). Find the topology generated on \( Y \) by the class \( Z \) of subsets of \( Y \) given that \( Z=\{\{a, b, c\},\{c, d\},\{d, e\}\} \)
Kenya Dec 17, 2024
Question 8 (1 point) When cold deep currents combine with warm surface currents in a loop that is called what? waves upwelling thermohaline circulation Question 9 (1 point) Which of the following separates layers of different density? thermocline pycnocline halocline
United States Dec 17, 2024
\( A=\{2,3,5,7\}, B=\{5,7,9,11\} \) бол \( A \cap B=? \)
Mongolia Dec 17, 2024
3. Seis amigos escalan una montaña. Martín está más abajo que Jimena, quien se encuentra un lugar más abajo que Linda. Deisy está más arriba que Martín, pero un lugar más abajo qué Adrián, quien está más abajo que Violetá, y esta se encuentra entre Jimena y Adrián. ¿Quién marcha penúltimo? \( \begin{array}{ll}\text { (A) Violeta } & \text { B) Deisy } \\ \text { (C) Jimena } & \text { (D) Martín }\end{array} \)
Peru Dec 17, 2024
2. Marcelo es más alto que Fernanda; Tomás es más alto que Fernanda, y Marcelo es menos alto que Tomás. ¿Quién es el más alto? \( \begin{array}{ll}\text { (A) Tomás } & \text { B Marcelo } \\ \begin{array}{ll}\text { (C) Fernanda } & \text { (D) Mario }\end{array}\end{array} \)
Peru Dec 17, 2024
Determine whether the variable is qualitative or quantitative. Model of car driven A. The variable qualitative or quantitative? B. The variable is qualitative because it is an attribute characteristic. C. The variable is qualitative because it is a numerical measure. D. The variable is quantitative because it is an attribute characteristic.
United States Dec 17, 2024
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