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Symbol Notation - Expert Level: operational symbols EXPERT

Strategic basic drills ★ for symbol notation: 20 expert-level problems. Worksheet 29 of 30 - Focus: operational symbols. Develop expertise in symbolic logic, notation puzzles, symbol interpretation with step-by-step solutions. Ideal for expert-level learners targeting challenging problems and time-bound practice.

📝 Worksheet 29 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Expert level

What you'll learn in this worksheet:
Your progress through Symbol Notation
Worksheet 29 of 30 (96% complete)

Question 1

If P = False, Q = True, and 'nor' means NOR, then evaluate: P nor Q
Logical operation: NOR
P=False, Q=True → NOR is True only when both are False
Result: False
logic, boolean

Question 2

If f(x)=x+2, g(x)=2x, h(x)=x², p(x)=x-3, q(x)=x/2, r(x)=3x-1, then evaluate: r(f(g(6)))
Evaluate from innermost outward:
r(f(g(6)))
= 327
nested, functions, advanced

Question 3

If k(x) = x + 2x, then find k(10)
Substituting x = 10:
10 + 210 = 220
functions, substitution

Question 4

Given: A = {1, 4, 5, 7, 9, 10} B = {1, 2, 5, 7} C = {1, 5, 10} Find: B ∩ C
Intersection of B and C:
{1, 2, 5, 7} ∩ {1, 5, 10} = {1, 5}
sets, operations

Question 5

If f(x)=x+2, g(x)=2x, h(x)=x², p(x)=x-3, q(x)=x/2, r(x)=3x-1, then evaluate: f(q(g(5)))
Evaluate from innermost outward:
f(q(g(5)))
= 14.50
nested, functions, advanced

Question 6

If ⊕ = +, ∆ = + (standard order of operations applies), then evaluate: 9 ⊕ 8 ∆ 1
Substituting symbols: 9 + 8 + 1
Applying order of operations: = 18
arithmetic, basic

Question 7

If P = False, Q = False, and '<->' means IFF, then evaluate: P <-> Q
Logical operation: IFF
P=False, Q=False → IFF is True when both are same
Result: True
logic, boolean

Question 8

If h(x) = x² - x, then find h(10)
Substituting x = 10:
10² - 10 = 90
functions, substitution

Question 9

If '≠' means '≠', then determine: 1 ≠ 18
≠ = ≠
1 ≠ 18 is True
inequality, comparison

Question 10

If f(x)=x+2, g(x)=2x, h(x)=x², p(x)=x-3, q(x)=x/2, r(x)=3x-1, then evaluate: h(p(g(6)))
Evaluate from innermost outward:
h(p(g(6)))
= 529
nested, functions, advanced

Question 11

Given matrices: A = [ 1 2] [ 4 5] B = [ 2 5] [ 5 3] Compute: A × B
Matrix multiplication:
A × B =

[12 11]
[33 35]
matrix, advanced

Question 12

If f(x)=x+2, g(x)=2x, h(x)=x², p(x)=x-3, q(x)=x/2, r(x)=3x-1, then evaluate: g(r(4))
Evaluate from innermost outward:
g(r(4))
= 233
nested, functions, advanced

Question 13

Given: A = {3, 5, 7} B = {3, 4, 5, 6, 8, 9} C = {1, 3, 5, 6, 8, 10} Find: C − B
Difference of C and B:
{1, 3, 5, 6, 8, 10} − {3, 4, 5, 6, 8, 9} = {1, 10}
sets, operations

Question 14

If ♧ = ×, ☆ = - (standard order of operations applies), then evaluate: 9 ♧ 4 ☆ 11
Substituting symbols: 9 × 4 - 11
Applying order of operations: = 25
arithmetic, basic

Question 15

In the notation system where ♠ means x - 3, what is the value of ♠(7)?
Applying ♠ to 7:
7 - 3 = 4
complex, systems

Question 16

If P = True, Q = True, and 'nor' means NOR, then evaluate: P nor Q
Logical operation: NOR
P=True, Q=True → NOR is True only when both are False
Result: False
logic, boolean

Question 17

If f(x)=x+2, g(x)=2x, h(x)=x², p(x)=x-3, q(x)=x/2, r(x)=3x-1, then evaluate: p(q(3))
Evaluate from innermost outward:
p(q(3))
= -1.50
nested, functions, advanced

Question 18

Given matrices: A = [ 2 3] [ 2 2] B = [ 5 1] [ 2 5] Compute: A + B
Matrix addition:
A + B =

[ 7 4]
[ 4 7]
matrix, advanced

Question 19

Given: A = {2, 3, 5, 8, 9, 10} B = {1, 3, 4, 7, 8, 9} C = {1, 3, 6, 7, 9} Find: A − B
Difference of A and B:
{2, 3, 5, 8, 9, 10} − {1, 3, 4, 7, 8, 9} = {2, 5, 10}
sets, operations

Question 20

In the notation system where ◆ means 2x + 1, what is the value of ◆(3)?
Applying ◆ to 3:
23 + 1 = 24
complex, systems
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