Given the set, A = {-4, -2, 0, 2, 4, 6}, what are the members of x in the proposition,(∃𝑥 ∈ 𝐴)(𝑥 + 2 ≤ 5)
Question
Given the set, A = {-4, -2, 0, 2, 4, 6}, what are the members of x in the proposition,
Solution
The proposition (∃𝑥 ∈ 𝐴)(𝑥 + 2 ≤ 5) translates to "There exists an x in set A such that x + 2 is less than or equal to 5".
To find the members of x that satisfy this condition, we need to subtract 2 from both sides of the inequality, which gives us x ≤ 3.
Now, we compare this result with each member of set A to find the members that satisfy the condition.
-4 + 2 = -2, which is less than 3. So, -4 is a member. -2 + 2 = 0, which is less than 3. So, -2 is a member. 0 + 2 = 2, which is less than 3. So, 0 is a member. 2 + 2 = 4, which is less than 3. So, 2 is not a member. 4 + 2 = 6, which is less than 3. So, 4 is not a member. 6 + 2 = 8, which is less than 3. So, 6 is not a member.
Therefore, the members of x in the proposition (∃𝑥 ∈ 𝐴)(𝑥 + 2 ≤ 5) are -4, -2, and 0.
Similar Questions
The solution set of x^2 + 5x + 6 = 0Question 1Answera.∅b.{-1 ,6 }c.{-2 ,-3 }d.{2 ,3 }
If A = {1, 2, 3, 4, 5} , B = {a, b, c, d, e} and C = { -, +, x, @, *} , then which of the following is the not the element of set (A x B x C)?
Let S={x∈R :x≥0 & 2∣∣x√−3∣∣+x√ (x√−6)+6=0} . Then S:Contains exactly four elementsIs an empty setContains exactly one elementContains exactly two elements
Determine whether the Relation R in the set A=1,2,3,4,5,6 as R={(x,y):yisdivisiblebyx} is reflexive, symmetric and transitiveHard
f A={1,4,5} and the relation R defined on the set A as aRb if a+b < 6 checkwhether the relation R is an equivalence relation
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.