Suppose that Q(x) is the statement \"x + 1 = 2x.\" What are the truth values of
ID: 3806604 • Letter: S
Question
Suppose that Q(x) is the statement "x + 1 = 2x." What are the truth values of Forall xQ(x) and 3xQ(x)? Suppose the variable x represents students and y represent course, and: U(y):y is an upper-level course M(y):y is a math course F(x):x is a freshman B(x):x is a full-time student T(x, y): student x is taking course y Write the statement using these predicates and any needed quantifiers. (a) Michael is taking MAT 281 (b) All students are freshmen. (c) Every student is a full-time student. (d) No math course is upper-level.Explanation / Answer
x Q(x) means for all x it is true that “x+1=2x”
but if we consider x = 2, “2+1 = 4” is false
Therefore x Q(x) is false
x Q(x) means there exist at least a x for which “x+1=2x” is true
so if we consider x = 1,w have “1+1 = 2*1” which is is true
Therefore x Q(x) is true
4.
Please note that ¬ y M(y)àU(y) is not valid because for the statement to be valid, M(y)àU(y) must always be false, but if a subject is not Maths, M(y)àU(y) become true, hence contradicting.