17-letter words containing educ
- deductible clause — a clause in an insurance policy stipulating that the insured will be liable for a specified initial amount of each loss, injury, etc., and that the insurance company will be liable for any additional costs up to the insured amount.
- deduction theorem — the property of many formal systems that the conditional derived from a valid argument by taking the conjunction of the premises as antecedent and the conclusion as consequent is true
- deductive tableau — (tool) A theorem proof system consisting of a table whose rows contain assertions or goals. Variables in assertions are implicitly universally quantified and variables in goals are implicitly existentially quantified. The declarative meaning of a tableau is that if every instance of every assertion is true then some instance of at least one of the goals is true.
- education contact — (job) The person at a company who should receive educational material.
- further education — adult education.
- liberal education — an education based primarily on the liberal arts, emphasizing the development of intellectual abilities as opposed to the acquisition of professional skills.
- natural deduction — (logic) A set of rules expressing how valid proofs may be constructed in predicate logic. In the traditional notation, a horizontal line separates premises (above) from conclusions (below). Vertical ellipsis (dots) stand for a series of applications of the rules. "T" is the constant "true" and "F" is the constant "false" (sometimes written with a LaTeX \perp). "^" is the AND (conjunction) operator, "v" is the inclusive OR (disjunction) operator and "/" is NOT (negation or complement, normally written with a LaTeX \neg). P, Q, P1, P2, etc. stand for propositions such as "Socrates was a man". P[x] is a proposition possibly containing instances of the variable x, e.g. "x can fly". A proof (a sequence of applications of the rules) may be enclosed in a box. A boxed proof produces conclusions that are only valid given the assumptions made inside the box, however, the proof demonstrates certain relationships which are valid outside the box. For example, the box below labelled "Implication introduction" starts by assuming P, which need not be a true proposition so long as it can be used to derive Q. Truth introduction: - T (Truth is free). Binary AND introduction: ----------- | . | . | | . | . | | Q1 | Q2 | ----------- Q1 ^ Q2 (If we can derive both Q1 and Q2 then Q1^Q2 is true). N-ary AND introduction: ---------------- | . | .. | . | | . | .. | . | | Q1 | .. | Qn | ---------------- Q1^..^Qi^..^Qn Other n-ary rules follow the binary versions similarly. Quantified AND introduction: --------- | x . | | . | | Q[x] | --------- For all x . Q[x] (If we can prove Q for arbitrary x then Q is true for all x). Falsity elimination: F - Q (Falsity opens the floodgates). OR elimination: P1 v P2 ----------- | P1 | P2 | | . | . | | . | . | | Q | Q | ----------- Q (Given P1 v P2, if Q follows from both then Q is true). Exists elimination: Exists x . P[x] ----------- | x P[x] | | . | | . | | Q | ----------- Q (If Q follows from P[x] for arbitrary x and such an x exists then Q is true). OR introduction 1: P1 ------- P1 v P2 (If P1 is true then P1 OR anything is true). OR introduction 2: P2 ------- P1 v P2 (If P2 is true then anything OR P2 is true). Similar symmetries apply to ^ rules. Exists introduction: P[a] ------------- Exists x.P[x] (If P is true for "a" then it is true for all x). AND elimination 1: P1 ^ P2 ------- P1 (If P1 and P2 are true then P1 is true). For all elimination: For all x . P[x] ---------------- P[a] (If P is true for all x then it is true for "a"). For all implication introduction: ----------- | x P[x] | | . | | . | | Q[x] | ----------- For all x . P[x] -> Q[x] (If Q follows from P for arbitrary x then Q follows from P for all x). Implication introduction: ----- | P | | . | | . | | Q | ----- P -> Q (If Q follows from P then P implies Q). NOT introduction: ----- | P | | . | | . | | F | ----- / P (If falsity follows from P then P is false). NOT-NOT: //P --- P (If it is not the case that P is not true then P is true). For all implies exists: P[a] For all x . P[x] -> Q[x] ------------------------------- Q[a] (If P is true for given "a" and P implies Q for all x then Q is true for a). Implication elimination, modus ponens: P P -> Q ---------- Q (If P and P implies Q then Q). NOT elimination, contradiction: P /P ------ F (If P is true and P is not true then false is true).
- nursery education — education provided at a school for young children, usually from three to five years old
- primary education — junior, elementary schooling
- private education — education provided by a private individual or organization, rather than by the state or a public body
- psychoeducational — designating or of psychological methods, as intelligence tests, used in evaluating learning ability
- reduce to silence — If someone or something reduces you to silence, they make you feel so upset or confused that you cannot speak.
- reduction formula — a formula, such as sin (90° ± A) = cos A, expressing the values of a trigonometric function of any angle greater than 90° in terms of a function of an acute angle
- special education — education that is modified or particularized for those with singular needs, as disabled or maladjusted people, slow learners, or gifted children.
- teacher education — training to become a teacher, usually at an institution of higher education
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