Suppose you want to design a version of the propose-and-reject algorithm that avoids the property of guaranteed women-pessimality. Identify valid strategies from the following list that would accomplish this goal without compromising the guarantee of a stable matching. Let X be the set of proposing entities and Y be the set of passive entities (entities receiving proposals). i.) Swap the contents of X and Y . ii.) Allow bilateral proposals from both X and Y . iii.) Shuffle the contents of X and Y and partition the set at index | X |

Asolar eclipse occurs when the moon gets between earth and the sun, and the moon casts a shadow over earth. a solar eclipse can only take place at the phase of new moon, when the moon passes directly between the sun and earth and its shadows fall upon earth's surface.

Part (a) is relatively straight forward.there are 4 aces in a standard 52-card deck. so the probability that an ace is picked is just 4/52.part (b): note that there are 4 suits in a standard 52-card deck. so picking hearts will be 13/52 or 1/4.part (c): the probability condition or means we need to add the two probabilities because we do not want them simultaneously. so, we end up getting pr(ace) + pr(heart).from part (a), we found that picking an ace had a probability of 4/52, which is reduced down to 1/13.from part (b), we found that picking a heart had a probability of 1/4.so, the probability of an ace or a heart is 1/13 + 1/4 = 4/52 + 13/52 = 17/52.

With reference to the solutions, following things may be noted1) homogeneous solutions comprises of single phase.2) heterogeneous solution comprises of more than one phase.3) in colloidal solution, solute is evenly distributed in solvent. in such system, it is difficult to separate solute and solvent.4) in suspension, there is an uneven distribution of solute in solvent. in such system, solute and solvent gets separated on standing long.    blood is a homogeneous and colloidal solution,salad dressing is a heterogeneous and suspension solution.