In 1937, Claude Shannon showed that computer scientists could use symbolic logic to design computer circuits by using the following approach. Electricity passes through a switch when it is closed and does not flow when the switch is open. Open switch Closed switch As shown in the following diagram, electricity flows through a series circuit only when switches p and q are both closed. A series circuit corresponds to a conjunction, p ∧ q , in logic. A parallel circuit corresponds to disjunction, p ∨ q . Electricity will flow through a parallel circuit if either p or q is closed. Series circuit Parallel circuit We can build more complicated circuits by combining series and parallel circuits. In Exercises 55 − 58 , write the logical form that corresponds to each of the following circuits.
In 1937, Claude Shannon showed that computer scientists could use symbolic logic to design computer circuits by using the following approach. Electricity passes through a switch when it is closed and does not flow when the switch is open. Open switch Closed switch As shown in the following diagram, electricity flows through a series circuit only when switches p and q are both closed. A series circuit corresponds to a conjunction, p ∧ q , in logic. A parallel circuit corresponds to disjunction, p ∨ q . Electricity will flow through a parallel circuit if either p or q is closed. Series circuit Parallel circuit We can build more complicated circuits by combining series and parallel circuits. In Exercises 55 − 58 , write the logical form that corresponds to each of the following circuits.
Solution Summary: The author explains the logical form of the given circuit.
In 1937, Claude Shannon showed that computer scientists could use symbolic logic to design computer circuits by using the following approach. Electricity passes through a switch when it is closed and does not flow when the switch is open.
Open switch
Closed switch
As shown in the following diagram, electricity flows through a series circuit only when switches p and q are both closed. A series circuit corresponds to a conjunction,
p
∧
q
,
in logic. A parallel circuit corresponds to disjunction,
p
∨
q
.
Electricity will flow through a parallel circuit if either p or q is closed.
Series circuit
Parallel circuit
We can build more complicated circuits by combining series and parallel circuits.
In Exercises
55
−
58
,
write the logical form that corresponds to each of the following circuits.
The probability of being born in a particular month is about 1:12. Determine the probability of not being born in September. Express this ratio as a fraction, a decimal, a percent and in words.
In his first hockey game of the season, Brayden takes a total of 10 shots on the goalie and scores 1 time. Later in the season, he takes 30 shots in total on the goalie. How many goals would you expect him to make? What assumptions are making? Are your assumptions realistic? Explain.
The probability of being born in a particular month is about 1:12. Determine the probability of not being born in September. Express this ratio as a fraction, a decimal, a percent and in words.
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