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# Lesson 14

## Logical Operators¶

This lesson covers:

• Basic logical operators
• Compound operators
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# Setup: Reproducible random numbers

import numpy as np
rs = np.random.RandomState(20000101)


### Problem: Basic Logical Statements¶

Create the variables (in order)

• x as rs.random_sample(), a uniform on $[0, 1)$
• y as rs.standard_normal(), a standard normal ($N(0,1)$)
• z as rs.randint(1, 11), a uniform random integer on $[1, 2,\ldots, 10]$

Check whether each of these are above their expected value.

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### Problem: Using comparison operators¶

1. Check if z is 7
2. Check is z is not 5
3. Check if z is greater than or equal to 9
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### Problem: Combining booleans¶

1. Determine if $2\leq z < 8$
2. Determine if $z < 2 \cup z \geq 8$ using or
3. Rewrite 2 using not and your result from 1.
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### Exercises¶

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# Setup: Data for Exercise
import numpy as np
rs = np.random.RandomState(19991213)

# Like range, lower included, upper excluded
# u in (0, 1, 2, ..., 5)
u = rs.randint(0, 6)
# v in (-2, -1, 0, 1, 2)
v = rs.randint(-2, 3)

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#### Exercise¶

Is the product $uv$ 0 and only one of $u$ and $v$ is 0?

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#### Exercise¶

Write three logical statements that will determine if $0\leq u \leq 2$ and $0\leq v \leq 2$.

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