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3 years ago

The sum of two numbers is -63 the first number minus the second number is -41 find the numbers

Mathematics

1 answer:

Ivenika [448]3 years ago

3 0

Answer:

x = -52

y = -11

Step-by-step explanation:

Let 1st number = x

Let 2nd number = y

Hence:

x+y=-63

x-y=-41

y = x+41

(Apply Simultaneous Equations)

x+(x+41)=-63

2x+41=-63

2x=-63-41

2x=-104

x=-104/2

x=-52

Now:

y=-52+41

y=-11

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Translate each of these statements into logical expressions by using quatifiers and predicates with one or two variables. (a) A

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a) $A = \{\exists x \in M, \exist y \in U\,|\,xGy \}$ , b) $B = \{\exists x \in M,\,\exists y \in H\,|\,xMy \}$ , c) $C = \{\forall x \in M\,|\,xI \}$ , d) $D = \{\exists x \in M,\,\forall y \in U\,|\,xJy \}$ , e) $E = \{\exists x \in M, \forall y \in V, V \subseteq U\,|\,xJy \}$

Step-by-step explanation:

a) x - A student, M - Set of students of discrete math class, G - has lived in, y - Florida, U - Set of states of the United States of America.

$A = \{\exists x \in M, \exist y \in U\,|\,xGy \}$

b) x - A student, M - Set of students of discrete math class, y - A perfect grade, H - Midterm I.

$B = \{\exists x \in M,\,\exists y \in H\,|\,xMy \}$

c) x - A student, M - Set of students of discrete math class, I - loves discrete math.

$C = \{\forall x \in M\,|\,xI \}$

d) x - A student, M - Set of students of discrete math class, J - has been in, y - a state, U - Set of states of the United States of America.

$D = \{\exists x \in M,\,\forall y \in U\,|\,xJy \}$

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$E = \{\exists x \in M, \forall y \in V, V \subseteq U\,|\,xJy \}$

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