ﻓﺮﺽ ﻣﺤﺮﻭﺱ 1
ﺙ ﺍﻻﺩﺍﺭﺳﺔ ﻓﺎﺱ
ﻧﻌﺘﺒﺮ ﺍﻟﻌﺒﺎﺭﺗﻴﻦ
ﺍﻟﺘﻤﺮﻳﻦ ﺍﻷﻭﻝ
P
:
Q
:
(1ﺣﺪﺩ ﻧﻔﻲ ﻛﻞ ﻣﻦ
P
2 y +1
y
ﻭ
P
=x
1
4
) ( ∀x ∈ ℝ
≥ x2
) ( ∃y ∈ ℝ
) ( ∀x ∈ ℝ
*
/
(2ﺣﺪﺩ ﺣﻘﻴﻘﺔ ﻛﻞ ﻣﻦ P
Q
x+ y+2
y =1ﻭ ⇔ x =1
2
-2ﺃ -ﺑﻴﻦ ﺑﻔﺼﻞ ﺍﻟﺤﺎﻻﺕ ﺃﻥ
x + x2 +1 ≻ 0
ﺏ -ﺑﻴﻦ ﺃﻥ
4n 2 + 8n + 3 ∉ ℕ
-4ﺃ -ﺑﻴﻦ ﺑﺎﻟﺘﺮﺟﻊ ﺃﻥ
ﺏ -ﺑﺎﻟﺘﺮﺟﻊ ﺍﺳﺘﻨﺘﺞ ﺃﻥ
ﺍﻟﺗﻣﺭﻳﻥ ﺍﻟﺛﺎﻟﺙ Aﻭ
ﻋﺪﺩ ﺯﻭﺟﻲ
) ( ∀n ∈ ℕ
B
ﻭ
⇒ B⊂C
A ∩ C = ∅ -2
) ( ∀n ∈ ℕ
*
∅≠E
E⊂F
E
( A ∩ B ) ∩ ( A ∩ C ) ∪ A
A∩ B ⊂ A∪C
ﻭ
-3ﻫﻝ
A∪ B ⊂ A∪C
}B = {2k : k ∈ ℤ
ﻭ
-3ﺑﻳﻥ ﺃﻥ A ∩ ℤ = A ∩ B
1
ﺍﻟﺗﻣﺭﻳﻥ ﺍﻟﺧﺎﻣﺱ E = ( x, y ) ∈ ℝ 2 ; x 2 + y 2 − ( x + y ) = −
4
-2ﺑﻳﻥ ﺃﻥ
2
) ∀ ( x; y ) ∈ ( ℝ
( ∀n ∈ ℕ ) :
8k
A=
ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺮﺍﺑﻊ ﻧﻌﺘﺒﺮ ﺍﻟﻤﺠﻤﻮﻋﺎﺕ ﺍﻟﺘﺎﻟﻴﺔ : k ∈ℤ
2k +1
-1ﺑﻴﻦ ﺃﻥ 16 ∉ A
2
( ∀x ∈ ℝ ) :
Cﺃﺟﺯﺍء ﻣﻥ ﻣﺟﻣﻭﻋﺔ
)A∩ B ∩C ∩(B ∪C
-2ﺑﻳﻥ ﺃﻥ
∀ ( x; y ) ∈ ( ℝ + ) :
1 + 2 × 3n −1 + 5nﻳﻘﺑﻝ ﺍﻟﻘﺳﻣﺔ ﻋﻠﻰ 8
*
ﻭ
3n −1 + 5n
ﻭ Qﻋﻠﻞ ﺟﻮﺍﺑﻚ
= x+ y
x ≠ y ⇒ x + x2 +1 = y + y2 +1
-3ﺑﻴﻦ ﺑﺎﻟﺨﻠﻒ ﺃﻥ
-1ﺗﺣﻘﻕ ﺃﻥ
1ﺭﻳﺎﺿﻲ
ﺣﻴﺚ
] x ∉ [ −2; 2ﺃﻭ
ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺜﺎﻧﻲ -1ﺑﻴﻦ ﺃﻥ
-1ﺑﺳﻁ
ﻭ Q
ﻛﺮﻭﻡ ﺭﺷﻴﺪ
ﻭ
-4ﺣﺩﺩ ﺑﺗﻔﺻﻳﻝ A ∩ ℤ
]F = [ 0,1] × [ 0,1
F⊂E
ﻭ
}C = {2k + 1: k ∈ ℤ
ﻋﻠﻝ ﺟﻭﺍﺑﻙ