1.2.3 Ejercicios de cuantificadores Ejercicio 1.22. En cada una de las siguientes proposiciones, identi- fica el predicado, nómbralo (como \( P(x), Q(n) \), etc.) y reescribe la proposición usando los símbolos \( \exists \), \( \exists 1 \) y \( \forall \) apropiadamente. a) Existe un número positivo \( x \) tal que \( x^{2}=5 \). b) Para cualquier \( n \), el número \( 2 n+1 \) es impar. c) Para toda \( k \) existe \( t \) tal que \( t=\frac{1}{k} \). d) Existe exactamente un número \( x \) tal que \( 5+x=7 \). e) Para todo número positivo \( n \), tenemos que \( n+1>n \). Ejercicio 1.23. Escribe la negación de cada una de las siguientes roposiciones. a) \( 7 \leq 10 \). b) No es cierto que \( 1+2=4 \). c) El cuadrado de 5 no es 16 . d) Ningún político es honesto. e) Existe un político que es deshonesto. f) Para algún número real \( x \), se cumple que \( x^{2}+3 x-2=0 \). g) Para cualquier número real \( x \), se cumple que \( x+1 \leq 0 \). h) Existe un número natural \( n \) tal que para todo número natural \( m \) se cumple que \( n \leq m \).

A piece of metal weighing 62.77 g was heated to \( 50.00^{\circ} \mathrm{C} \) and then put it into 50.00 g of water initially at \( 11.90^{\circ} \mathrm{C} \). The metal and water were allowed to come to an equilibrium temperature, determined to be \( 16.00^{\circ} \mathrm{C} \). Assuming no heat lost to the environment, the specific heat of metal was calculated to be [C] \( \frac{\mathrm{J}}{\mathrm{g}^{\circ} \mathrm{C}} \cdot \mathrm{C}_{\text {water }}=4.184 \mathrm{~J} / \mathrm{gC} \) Please enter only the number in standard notation (not scientific notation) in the blank. Do not include the unit.

Next question \( \rightleftarrows \) Get a similar question You can retry this question bel Fully simplify the following expression: \( \sqrt{-405} \). Submit Question

Set the values of \( \mathrm{a}=4 \) and \( \mathrm{b}=1 \) using the a and b -sliders. Check the Point box and move the \( x \)-slider to \( x=3 \). Notice that \( (3,1) \) is currently a point on the curve. Use the c -slider to find the value of c that will result in the point \( (3,4) \) being on the curve. Use the interactive figure to find your answer. Use the left and right arrow keys to move along a slider as needed. Click here to launch the interactive figure.

The population of rats, R(t), in a small town's sewage system \( t \) years after the beginning of the year 2000 is given by \( R(t)=4900 e^{0} \) osst . Find the AVERAGE population of rats in the system from the beginning of the year 2002 to the beginning of the year 2010 . ROUND YOUR FINAL.ANSWER TO THE NEAREST RAT. The average popualtion was about \( \square \) rats.

Question 2 According to algebraic laws, wh the following statements are th a) \( 145+653=653+145 \) b) \( (78 \times 2) \times 6=78 \times(2 \times 6) \) c) \( 20(7+x)=140+20 x \)