I have the following question and I wondered if there was any way to do this easier and faster, I find that it takes me a while to find the solutions In each of the following, two open sentences P(x) and Q(x) over a domain S are given. Determine all x ESfor which P(x) ⇒ Q(x) is a true statement.(a) P(x) : x 3 = 4; Q(x) : x ≥ 8; S = R.-(b) P(x) : x² ≥ 1; Q(x) : x ≥ 1; S = R.|(c) P(x): x² ≥ 1; Q(x) : x ≥ 1; S = N.(d) P(x) : x € [−1, 2]; Q(x) : x² ≤ 2; S = [−1, 1].

As per bartleby guidelines we solve to only first three subpart and rest part can be reposted…

In each of the following, two open sentences P(x) and Q(x) over a domain S are given. Determine all x ES for which P(x) ⇒ Q(x) is a true statement. (a) P(x) : x 3 = 4; Q(x) : x ≥ 8; S = R. (b) P(x): x² ≥ 1; Q(x) : x ≥ 1; S = R.| (c) P(x): x² ≥ 1; Q(x) : x ≥ 1; S = N. (d) P(x) : x = [1, 2]; Q(x): x² < 2; S = [1,1].