Math Quiz: Math for - Nested Conditional Statements

1. Reactor Safety System: A safety system for a chemical reactor monitors temperature $T$ (in $^{\circ}$C) and pressure $P$ (in kPa). The system follows these rules:

   • First, it checks if $T < 150^{\circ}$C.
   • If $T < 150^{\circ}$C is true, it then checks if $P < 1000$ kPa.
     • If $P < 1000$ kPa is also true, the system state is 'Stable'.
     • Else (if $P \geq 1000$ kPa), the system state is 'Warning: High Pressure'.
   • Else (if $T \geq 150^{\circ}$C), the system state is 'Danger: High Temperature'.

   Determine the system state for:

   1. $T = 120^{\circ}$C, $P = 900$ kPa

      Answer (a):

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   2. $T = 140^{\circ}$C, $P = 1100$ kPa

      Answer (b):

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   3. $T = 160^{\circ}$C, $P = 950$ kPa

      Answer (c):

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2. Automated Irrigation System: An automated irrigation system waters a field based on soil moisture $M$ (as a percentage) and the probability of rain $R$ (as a percentage) in the next 24 hours. The rules are:

   • If $M < 30\%$:
     • If $R < 20\%$, water for 60 minutes.
     • Else (if $R \geq 20\%$), water for 30 minutes.
   • Else if $M \geq 30\%$ and $M \leq 60\%$:
     • If $R < 50\%$, water for 15 minutes.
     • Else (if $R \geq 50\%$), do not water.
   • Else ($M > 60\%$):
     • Do not water.

   Determine the watering time if:

   1. Soil moisture is $25\%$ and probability of rain is $10\%$.

      Answer (a):

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   2. Soil moisture is $40\%$ and probability of rain is $60\%$.

      Answer (b):

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   3. Soil moisture is $20\%$ and probability of rain is $30\%$.

      Answer (c):

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3. Conditional Logic Evaluation: Let $x, y$ be integers. Consider the conditions: C1: $x > 0$
   C2: $y < x$
   C3: $x \text{ is even}$
   An item's inspection follows these rules:

   • If C1 is false, the outcome is 'Fail: C1'.
   • Else (C1 is true):
     • If C2 is false, the outcome is 'Fail: C2'.
     • Else (C2 is true):
       • If C3 is false, the outcome is 'Fail: C3'.
       • Else (C3 is true), the outcome is 'Pass'.

   Determine the outcome for:

   1. $x = 4, y = 2$

      Answer (a):

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   2. $x = 5, y = 3$

      Answer (b):

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   3. $x = -2, y = -5$

      Answer (c):

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   4. $x = 6, y = 8$

      Answer (d):

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4. Compound Statement Truth Value: Evaluate the truth of the statement:
   "If ($A > 5$ AND $A < 15$), then ($A \text{ is even}$ OR $A \text{ is a multiple of } 3$)"
   for the following integer values of $A$:

   1. $A = 6$

      Answer (a):

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   2. $A = 7$

      Answer (b):

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   3. $A = 10$

      Answer (c):

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   4. $A = 4$ (Hint: An "If P, then Q" statement is true if P is false.)

      Answer (d):

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5. Number Classification Logic: A number $N$ is classified based on two properties:

   1. Is $N$ a multiple of 5? (Let this be P1)
   2. Is $N$ less than 20? (Let this be P2)

   Describe a set of rules using a nested "If...Then...Else..." structure to classify $N$ into one of four categories. Your description should clearly show the decision-making process, for example, by first checking P1, and then based on that result, checking P2.

   • Category Alpha: P1 is true AND P2 is true.
   • Category Beta: P1 is true AND P2 is false.
   • Category Gamma: P1 is false AND P2 is true.
   • Category Delta: P1 is false AND P2 is false.

   Your Answer (Describe rules):

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