Sentence examples for implication the following from inspiring English sources

The first principles of logic are simply ${\vdash}1 $and ${\dashv}0 $but to indicate the tabulation for implication the following principles must be adhered to: ${\vdash}C00, {\vdash}C01, {\dashv}C10, {\vdash}C11$.

I think I may have gasped when I finally caught up on the implications of the following statement about Freda and Brenda's sharing a sleeping space in their dingy bedsit: Brenda had fashioned a bolster to put down the middle of the bed and a row of books to ensure that they lay less intimately at night.

The full article is here, but you can get a taste of the grim landscape and its dire health implications in the following two extracts: "The village secretary, Huang Jingxin, said: "Your hands start to itch as soon as you come into contact with the river water".

I present and discuss these implications in the following.

The implications of the following analysis will be that the entries in term-based entry groups can be classified as either non-identical as regards their concepts (homonyms, polysemes) or as identical.

Two strategies with serious implications are the following: One strategy in danger of failing suggests investors allocate the same percentage of an investor's nest egg to bonds as the investor's age.

These findings have implications for the following reasons.

Our findings have implications for the following reasons.

Our findings have implications for the following: 1) PCP solo management, 2)  nephrology co-management, and developing a systematic approach to  referral to nephrology.

The bifunction h : Γ × R n → R ∪ is said to be η-pseudomonotone on Γ if, for any x, y ∈ Γ, h ( x ; η ( y, x ) ) ≥ 0 ⇒ h ( y ; η ( x, y ) ) ≤ 0. The above implication is equivalent to the following implication: h ( y ; η ( x, y ) ) > 0 ⇒ h ( x ; η ( y, x ) ) < 0. Next, we present some properties for pseudoinvexity.

This implication holds for the following reasons.