Criticize the following proof by induction of the proposition, "happy families are all alike." consider a set consisting of one happy family. obvi- ously all its elements are the same. suppose it has been shown that for any set of n happy families, say {}, we have fi f2 ==fn. con- sider a set {f1. n+1} of n+1 happy families. then {f1.) is a set of n happy families, so f1 = f2 = = fn. similarly, {f2, f3, fn+1} is a set of n happy families, so fn+1 = = f2. thus fr+1 = fi also, and the set of n + 1 happy families are all alike. by the principle of induction, we see that for any finite set of happy families, they are all alike. since the set of all happy families is finite, we conclude: happy families are all alike.

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step-by-step explanation:

need more detail

step-by-step explanation:

lele

the correct option is:

b. a value of the variable that makes the polynomial equal to zero.

the root or roots of a polynomial are the values of the variable that makes the polynomial equal to 0. we can find the roots of a polynomial making the expression equal to 0 and then, isolating the variable (it it has just one variable).

for example, given the following polynomial:

the root or zero of the polynomial, can be found by making the expression equal to 0, and then, isolating the variable, so, finding the root we have:

therefore, we have that the root of the polynomial is equal to 2.

we must remember that the number of roots that a polynomial can have, will depend on the degree of the polynomial, a first degree polynomial have will have one single root, a second degree polynomial (quadratic expression) may have two roots and so.

hence the correct option is:

b. a value of the variable that makes the polynomial equal to zero.

have a nice day!

mariah is studying the life cycle of the monarch butterfly. she must choose one stage in the cycle to present in science class: egg, caterpillar, chrysalis, or adult. she plans to make her choice randomly using a custom spinner divided into four sections. first, however, she spins the spinner 50 times to see the frequencies it generates.

stage times landed on

egg 10

caterpillar 12

chrysalis 15

adult 13

step-by-step explanation: