uiveerit. . Express the following assertions using quantifiers. Specify the sets
ID: 3145092 • Letter: U
Question
uiveerit. . Express the following assertions using quantifiers. Specify the sets or N, etc.,) that the variables refer to, as needed. (a) 1,000,000 is not the largest number (b) The equation x2 + 1 = 0 does not have a real number solution. (c) 0 is less than every natural number (d) The equation 2.2 + a 0 has a real root for any negative real number a. (e) Every real number is a rational. 8. Express the following sentence symbolically. You can find a rational number between any two unequal real numbers. 9. Le t A be a subset of R. Write the negation of the following definition prouded teni Hint: A number b is not an upper bound for the set A provided that of the following assertion. Represent the statemen and its contraposition symbolically If a triangle is isosceles then it has tuo angles that are congruent to each othe
Explanation / Answer
Hi,
There are multiple questions in this, which is against chegg policy and we cannot answer more than one, so please post others as separate questions so that we can assist you :)
lets see the symbols we are going to use first,
- for all, - there exists, belongs to, -> implies, ¬ for negation,R for real number set, Z for integers, N for natural numbers
7.
a.1,000,000 is not the largest number i.e there are numbers greater than this, hence x, x>1000000, x R
b.x^2+1 doesnt have real roots,which is equivalent to writing, for any x in R, the equation wont satisfy i.e x, x^2+1!=0, x R
c. 0 less than every natural number, i.e every natural number is >0, x,x>0, x N
d.x^2+a=0 has real roots if a<0, a, a<0, such that x^2+a=0 a R-> x R
e.every real number is irrational
set of irrational is given by real numbers minus rational numbers(Q)
therefore x R -> x (R-Q)
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