(FP1) The exclusive or operation, denoted by ⊕ and sometimes known as XOR, is defined so that P ⊕Q is true iff P is true or Q is true, but not both. Prove (through a truth table, or otherwise) that for any statements P,Q,R: (a) ((P ⊕Q)⊕R)⇔ (P ⊕ (Q⊕R)) (b) (P ∧ (Q⊕R))⇔ ((P ∧Q)⊕ (P ∧R)) Answer. One could show both sentences were true through a truth table, either through showing the entire senten...

In 1985, Chor et al 2] conjectured that the only 1-resilient symmetric functions are the exclusive-or of all n variables and its negation. In this note the existence of symmetric resilient functions is shown to be equivalent to the existence of a solution to a simultaneous subset sum problem. Then, using arithmetic properties of certain binomial coeecients, an innnite class of counterexamples t...

While the global objective is exclusive breastfeeding (EBF) for a full 6 months duration, the standard indicator is a "prevalence" indicator, that is, the percentage of all children under age 6 months who are exclusively breastfed at a point in time. That yields a higher percentage than a more direct indicator of duration and can be easily misunderstood, exaggerating the amount of EBF. A measur...

We model competition between content distributors (platforms) for content providers, and show that whether or not content is exclusive or “multihomes” depends crucially on whether or not content providers maintain control over their own pricing to consumers: if content providers sell their content outright and relinquish control, they will tend to be exclusive; on the other hand, if content pro...