### 3.1 Sets & Set Diagrams

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• 17. Nuclear Weapons

A country's stockpile of nuclear weapons consists of operational warheads and reserve warheads. Information about the U.S. stockpile of nuclear weapons is shown. Draw a set diagram that shows the information. (See Example 5.)

U.S. Stockpile :

1968 strategic

500 nonstrategic

• Worked-Out Solution

There are 5113 warheads in total. Of these, some are operational warheads and some are reserve warheads.

Of the operational warheads, 1968 are strategic and 500 are nonstrategic.

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``` _    _     _____    _____       ___      _  __
| |  | ||  |  ___|| |  __ \\    / _ \\   | |/ //
| |/\| ||  | ||__   | |  \ ||  / //\ \\  | ' //
|  /\  ||  | ||__   | |__/ || |  ___  || | . \\
|_// \_||  |_____|| |_____//  |_||  |_|| |_|\_\\
`-`   `-`  `-----`   -----`   `-`   `-`  `-` --`

```
• 18. Nuclear Weapons

A country's stockpile of nuclear weapons consists of operational warheads and reserve warheads. Information about the U.S. stockpile of nuclear weapons is shown. How many reserve warheads are in the U.S. stockpile? (See Example 5.)

U.S. Stockpile :

1968 strategic

500 nonstrategic

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```  _____      ___      _____    _    _      _____
/ ____||   / _ \\   /  ___|| | || | ||   / ___//
/ //---`'  / //\ \\ | // __   | || | ||   \___ \\
\ \\___   |  ___  ||| \\_\ || | \\_/ ||   /    //
\_____|| |_||  |_|| \____//   \____//   /____//
`----`  `-`   `-`   `---`     `---`   `-----`

```
• 19. Russian Nuclear Weapons

• Intercontinental Ballistic Missiles (ICBMs)
• Submarine-Launched Ballistic Missiles (SLBMs)
• Bombers/Weapons

How many Russian operational warheads are nonstrategic?(See Example 6.)

• Worked-Out Solution

There are 4600 warheads total. Of these,

are strategic. This implies that

are nonstrategic.

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```  _____    __   __    ______     ___      _____
/  ___||  \ \\/ //  /_   _//   / _ \\   / ____||
| // __     \ ` //   `-| |,-   | / \ || / //---`'
| \\_\ ||    | ||      | ||    | \_/ || \ \\___
\____//     |_||      |_||     \___//   \_____||
`---`      `-`'      `-`'     `---`     `----`

```
• 20. Russian Nuclear Weapons

• Intercontinental Ballistic Missiles (ICBMs)
• Submarine-Launched Ballistic Missiles (SLBMs)
• Bombers/Weapons

Can you use this data to determine whether the United States or Russia has a greater stockpile of nuclear weapons? Explain your reasoning. (See Example 6.)

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``` _    _      ___     __   _     _____    _    _
| |  | ||   / _ \\  | || | ||  |  ___|| | || | ||
| |/\| ||  | / \ || | '--' ||  | ||__   | || | ||
|  /\  ||  | \_/ || | .--. ||  | ||__   | \\_/ ||
|_// \_||   \___//  |_|| |_||  |_____||  \____//
`-`   `-`   `---`   `-`  `-`   `-----`    `---`

```
• 21. Strategic Arms Reduction Treaty

In 2010, the United States ratified the New START (STrategic Arms Reduction Treaty) with Russia.  This agreement reduces the number of strategic nuclear weapons in each country.

1. How do you think New START will affect the set diagrams in Exercises 17–20?
2. Discuss trends in the graph. How do you think New START will affect the graph?

(See Example 6.)

• Worked-Out Solution
1. The set diagrams in Exercises 17 and 19 show that in 2010, the U.S. had 1968 strategic warheads and Russia had 2504 strategic warheads. Because START is an agreement to reduce strategic weapons, one would expect both of these numbers to drop.

2. During the Cold War (1950s and 1960s) between the United States and the USSR, the United States had a massive build-up of nuclear weapons. This reached a peak shortly after the Cuban Missile Crisis. The total number began to slowly decline until the collapse of the Soviet Union around 1990. With that collapse, the United States decreased its stockpile of nuclear weapons to around 10,000. Since then the number has slowly continued to decrease. With the signing of START, one would think that the number will decrease even further.

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``` __   __     ___      _____     _____    __   _
\ \\/ //   / _ \\   |__  //   |  ___|| | || | ||
\   //   | / \ ||    / //    | ||__   | '--' ||
/ . \\   | \_/ ||   / //__   | ||__   | .--. ||
/_//\_\\   \___//   /_____||  |_____|| |_|| |_||
`-`  --`   `---`    `-----`   `-----`  `-`  `-`

```
Ron Larson (author)1 decade ago |
Isn't this graph amazing! I was born in 1941. So, this graphs corresponds almost exactly to my time on Earth. I was going to high school during the height of the Cold War.
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• 22. Doomsday Clock

The Bulletin of the Atomic Scientists assesses how close humanity is to doomsday. Midnight represents doomsday. Do you think the minute hand is moving away from midnight, toward midnight, or neither? Explain your reasoning.

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```            ______   _    _      ___      _  _