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Symbol Notation - Beginner-Intermediate Level: symbolic reasoning BEGINNER-INTERMEDIATE

Strategic fast track practice for symbol notation: 20 beginner-intermediate-level problems. Worksheet 9 of 30 - Focus: symbolic reasoning. Develop expertise in notation puzzles, symbol interpretation, symbolic representation with step-by-step solutions. Ideal for developing learners targeting building on fundamentals with moderate challenges.

📝 Worksheet 9 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Beginner-intermediate level

What you'll learn in this worksheet:
Your progress through Symbol Notation
Worksheet 9 of 30 (30% complete)

Question 1

If P = True, Q = True, and '|' means OR, then evaluate: P | Q
Logical operation: OR
P=True, Q=True → OR gives True if at least one is True
Result: True
logic, boolean

Question 2

In the notation system where ◀ means x + 5, what is the value of ◀(8)?
Applying ◀ to 8:
8 + 5 = 13
complex, systems

Question 3

If '≈' means '≈', then determine: 12 ≈ 5
≈ = ≈
12 ≈ 5 (approximately equal) is False
inequality, comparison

Question 4

Given: A = {4, 6, 9} B = {6, 8, 9} C = {3, 6, 10} Find: C ∩ B
Intersection of C and B:
{3, 6, 10} ∩ {6, 8, 9} = {6}
sets, operations

Question 5

If '≻' means '>', then determine: 1 ≻ 4
≻ = >
1 > 4 is False
inequality, comparison

Question 6

If h(x) = 2x², then find h(9)
Substituting x = 9:
29² = 841
functions, substitution

Question 7

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: q(h(5))
Evaluate from innermost outward:
q(h(5))
= 12.50
nested, functions, advanced

Question 8

If ⊗ = ×, ♤ = - (standard order of operations applies), then evaluate: 7 ⊗ 5 ♤ 12
Substituting symbols: 7 × 5 - 12
Applying order of operations: = 23
arithmetic, basic

Question 9

Given matrices: A = [ 3 3] [ 2 5] B = [ 5 4] [ 2 2] Compute: A + B
Matrix addition:
A + B =

[ 8 7]
[ 4 7]
matrix, advanced

Question 10

If ★ = +, ♤ = - (standard order of operations applies), then evaluate: 5 ★ 6 ♤ 10
Substituting symbols: 5 + 6 - 10
Applying order of operations: = 1
arithmetic, basic

Question 11

In the notation system where ☀ means x³, what is the value of ☀(5)?
Applying ☀ to 5:
5³ = 125
complex, systems

Question 12

Given matrices: A = [ 1 5] [ 5 4] B = [ 1 4] [ 3 1] Compute: A + B
Matrix addition:
A + B =

[ 2 9]
[ 8 5]
matrix, advanced

Question 13

If g(x) = x² + 1, then find g(3)
Substituting x = 3:
3² + 1 = 10
functions, substitution

Question 14

If ♧ = ×, ◆ = × (standard order of operations applies), then evaluate: 1 ♧ 14 ◆ 8
Substituting symbols: 1 × 14 × 8
Applying order of operations: = 112
arithmetic, basic

Question 15

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(h(f(5)))
Evaluate from innermost outward:
r(h(f(5)))
= 348
nested, functions, advanced

Question 16

If k(x) = x - 8, then find k(2)
Substituting x = 2:
2 - 8 = -6
functions, substitution

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: r(q(6))
Evaluate from innermost outward:
r(q(6))
= 32
nested, functions, advanced

Question 18

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

Question 19

If ◊ = ×, ∇ = - (standard order of operations applies), then evaluate: 8 ◊ 9 ∇ 4
Substituting symbols: 8 × 9 - 4
Applying order of operations: = 68
arithmetic, basic

Question 20

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